4-1 Powers and Exponents - Welcome to Mrs. Summers's Websitemrssummersclass.weebly.com/uploads/9/1/9/5/9195204/... · Write each expression using exponents. 2 2 2 2 2 2 62/87,21 The

Write each expression using exponents.

1. 2 • 2 • 2 • 2 • 2 • 2

SOLUTION: The base 2 is a factor 6 times. So, the exponent is 6.

2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d

SOLUTION: The base d is a factor 6 times. So, the exponent is 6.

d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:

The base is a factor 3 times. So, the exponent is

3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)

SOLUTION: The base (y – 3) is a factor 3 times. So, the exponentis 3.

(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)

SOLUTION: The base (a + 1) is a factor 2 times. So, the exponentis 2.

(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2

7. The longhorn beetle can have a body length of over

24 centimeters. How many centimeters long is this?

SOLUTION:

The longhorn beetle can have a body length of over 16 cm.

ANSWER: 16 cm

8. Theo sends an e-mail to three friends. Each friend forwards the e-mail to three friends. Each of those friends forwards it to three friends, and so on. Find the number of e-mails sent during the fifth stage as a power. Then find the value of the power.

SOLUTION: The email is sent each time to 3 friends. So, the base is 3. During the 5th stage the exponent is 5.

So, the number of emails sent is 35.

ANSWER:

35; 243

Evaluate each expression if a = 3, b = –4, and c = 3.5.

9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57

Write each expression using exponents.13. 11 • 11 • 11 • 11


11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)

SOLUTION: The base (–8) is a factor 6 times. So, the exponent is6.

(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)

SOLUTION: The base (–14) is a factor 3 times. So, the exponent is 3.

(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:

The base is a factor 4 times. So, the exponent

is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)

SOLUTION: The base (–1.5) is a factor 3 times. So, the exponent is 3.

(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab

SOLUTION: The base ab is a factor 4 times. So, the exponent is 4.

ab • ab • ab • ab =(ab)4 or a

4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)

SOLUTION: The base (c + 4) is a factor 2 times. So, the exponentis 2.

8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)

SOLUTION: The base (n – 5) is a factor 3 times. So, the exponentis 3.

(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)

SOLUTION: The base (2x + 3y) is a factor 2 times. So, the exponent is 2.

(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2

25. The longest chain of active volcanoes is in the South

Pacific. This chain is more than 3 • 104 miles long

and has approximately 35 • 5 volcanoes.

a. How long is the chain of volcanoes? b. How many volcanoes are there?

SOLUTION: a.

The chain of volcanoes is 30,000 miles long.b.

There are 1215 volcanoes.

ANSWER: a. 30,000 mi b. 1215 volcanoes

26. A water park has a wave pool that contains about

26 • 4

3 • 10

2 gallons of water. How many gallons of

water is this?

SOLUTION:

The wave pool contains 409,600 gallons of water.

ANSWER: 409,600 gal

Evaluate each expression if x = –2, y = 3, and z = 2.5.

27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10

39. Be Precise The table shows the minimum areas of different sports fields.

a. Find the minimum area of each playing field. b. Order the areas from least to greatest. c. How much greater is the area of a field hockey field than the area of a men’s lacrosse field?

SOLUTION: a.

The minimum area for the Field Hockey field is

64,000 ft2.

The minimum area for the Men’s Lacrosse Field is

63,000 ft2.

The minimum area for the Women’s Soccer Field is

36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2

c. The difference is 64,000 ft2 – 63,000 ft

2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2

Evaluate each expression.

40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125

Replace each _ with <, >, or = to make a true statement.

52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >

58. Multiple Representations In this problem, you willexplore volume of a cube. The volume of a cube equals the side length cubed. a. Symbols Write an equation showing the relationship between side length s and volume V of a cube. b. Table Make a table of values showing the volumeof a cube with side lengths of 1, 2, 4, 8, and 16 centimeters. c. Analyze Use your table to make a conjecture about the change in volume when the side length of acube is doubled. Justify your response by writing an algebraic expression.

SOLUTION: a.

b.

c. When the side length is doubled, the volume of the cube is multiplied by 8. When the side is 4, the volume is 64. When the side is 8 (4 • 2), the volume is 512, which is equal to 8 • 64. If the side is doubled,

Side Length (cm)

Volume

(cm3)

1

2

4

8

16

then the new side is 2s.

ANSWER:

a. V = s3

b.

c. Sample answer: When the side length is doubled,

the volume of the cube is multiplied by 8. V = (2s)3 or

V = 8s3.

59. Model with Mathematics Write a real-world problem that involves multiplying two expressions with exponents. Then solve.

SOLUTION:

Sample answer: Jin drove 62 miles to visit a friend.

He drove 43 times as far to visit his uncle. How far

did he drive to visit his uncle?

2304 mi

ANSWER:



did he drive to visit his uncle? 2304 mi

60. Persevere with Problems Determine whether x3 is

always, sometimes, or never a positive number for x ≠ 0. Explain your reasoning.

SOLUTION:

x3 is sometimes a positive number for x ≠ 0. If x is

positive, then x3 is positive. If x is negative, then x

3 isnegative because the product of two negative numbers is always positive and the product of a positive number and a negative number is always negative. For example,

ANSWER:

Sometimes; if x is positive, then x3 is positive. If x is

negative, then x3 is negative because the product of

two negative numbers is always positive and the product of a positive number and a negative number is always negative.

61. Justify Conclusions Suppose the population of the United States is about 230 million. Is this number

closer to 107 or 10

8? Explain.

SOLUTION:

230 million is closer to 108. Sample answer: 10

7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is

much closer to 230,000,000 than 10,000,000.

ANSWER:

108; Sample answer: 10

7 =10,000,000 and 10

8 =

100,000,000. 100,000,000 is much closer to 230,000,000 than 10,000,000.

62. Identify Repeated Reasoning Use the pattern

below to predict the value of 50. Explain your

reasoning.

54 = 625

53 = 125

52 = 25

51 = 5

SOLUTION: The pattern shows that each number is found by

dividing the previous number by 5. 5 ÷ 5 = 1, so 50 =

1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:

50 = 1; Sample answer: Each number is found by


1.

63. Building on the Essential Question Describe the advantages of using exponents to represent numeric values.

SOLUTION: Using exponents is a more efficient way to describe and compare numbers, instead of having to write out each individual value many times.

ANSWER: Using exponents is a more efficient way to describe and compare numbers.

64. Marta observed that a bacterium cell doubled every 3minutes.

Which expression represents the number of cells after one half hour?

A 210

B 215

C 220

D 230

SOLUTION: The base is 2, and the exponent is equal to the time (in minutes) ÷ 3. So at one half hour, the time in minutes would be 30. Therefore, the exponent is 30 ÷3 = 10. So, the number of cells after one half hour is

210

. Choice A is correct.

ANSWER: A

65. Short Response Suppose a certain forest fire doubles in size every 8 hours. If the initial size of the fire was 1 acre, how many acres will the fire cover in 3 days?

SOLUTION:

Because the forest fire doubles each time, the base is2. The exponent is equal to the time in hours divided

by 8. In one day, or 24 hours, the fire is 23 = 8 acres.

In 3 days it will be 23 • 2

3 •2

3 = 8 • 8 • 8 = 512 acres.

Time (hours) Size of Fire (acres) 0 2

0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512

66. Which of the following is equivalent to 43 • 52

?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:

Choice H is correct.

ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:

Choice B is correct.

ANSWER: B

Find each sum or difference.68. –12 + (–7)

SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20

Name the property shown by each statement.74. 87 + 0 = 0

SOLUTION: When zero is added to any number, the sum is the number. This is the Additive Identity.

ANSWER: Additive Identity

75. 19 × 5 = 5 × 19

SOLUTION: The order of the numbers changed. This is the Commutative Property of Multiplication.

ANSWER: Commutative (×)

76. 12 • 0 = 0

SOLUTION: When any number is multiplied by zero, the product iszero. This is the Multiplicative Property of Zero.

ANSWER: Multiplicative Property of Zero

77. Kari grew inches last year and inches this

year. How many total inches did Kari grow in the past two years?

SOLUTION:

Kari grew a total of inches in the past two

years.

ANSWER:

in.

78. A dance instructor charges a sign-up fee of $50 plus $8 for each group lesson. Write an expression that can be used to find the total cost of dance lessons. Then find the cost of 15 lessons.

SOLUTION: Let d represent the number of dance lessons. To findthe total cost of d dance lessons, multiply d by 8 and add the sign-up fee of 50. So, the expression 50 + 8d can be used to find the total cost of dance lessons. To find the total cost of 15 lessons, replace d with 15in the expression 50 + 8d.

So, the total cost of 15 lessons is $170.

ANSWER: 50 + 8d; $170

Write the integer for each situation. Then identify its opposite and explain its meaning.

79. 150 below sea level

SOLUTION: Because it is 150 feet below sea level, the integer is –150. Its opposite is +150 or 150, which means 150 feet above sea level.

ANSWER: –150; +150 or 150; 150 feet above sea level

80. a profit of $75

SOLUTION: Because it is a profit of $75, the integer is +75 or 75.Its opposite is –75, which means a loss of $75.

ANSWER: +75 or 75; –75; a loss of $75

Find the greatest common factor for each pair ofnumbers.

81. 8 and 12

SOLUTION: Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12 The greatest common factor of 8 and 12 is 4.

ANSWER: 4

82. 18 and 24

SOLUTION: Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 The greatest common factor of 18 and 24 is 6.

ANSWER: 6

83. 12 and 14

SOLUTION: Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 14: 1, 2, 7, 14 The greatest common factor of 12 and 14 is 2.

ANSWER: 2

84. 27 and 36

SOLUTION: Factors of 27: 1, 3, 9, 27 Factors of 36: 1, 2, 4, 6, 9, 18, 36 The greatest common factor of 27 and 36 is 9.

ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80

SOLUTION: Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 The greatest common factor of 45 and 80 is 5.

ANSWER: 5

Find each quotient.87. –24 ÷ (–6)

SOLUTION: The quotient of two integers with the same sign is positive. So, –24 ÷ (–6) = 4.

ANSWER: 4

88. 60 ÷ (–4)

SOLUTION: The quotient of two integers with different signs is negative. So, 60 ÷ (–4) = –15.

ANSWER: –15

89. –56 ÷ 8

SOLUTION: The quotient of two integers with different signs is negative. So, –56 ÷ 8 = –7.

ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27

eSolutions Manual - Powered by Cognero Page 1

4-1 Powers and Exponents


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27




1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27


1. 2 • 2 • 2 • 2 • 2 • 2


2 • 2 • 2 • 2 • 2 • 2 = 26

ANSWER:

26

2. d • d • d • d • d • d


d • d • d • d • d • d = d6

ANSWER:

d6

3.

SOLUTION:


3.

ANSWER:

4. 4 • m • m • m • q • q • q

SOLUTION:

ANSWER:

4m3q

3

5. (y – 3)(y – 3)(y – 3)


(y – 3)(y – 3)(y – 3)= (y – 3)3

ANSWER:

(y – 3)3

6. (a + 1)(a + 1)


(a + 1)(a + 1)= (a + 1)2

ANSWER:

(a + 1)2



SOLUTION:


ANSWER: 16 cm




ANSWER:

35; 243


9. a3 + 2

SOLUTION:

ANSWER: 29

10. 3(b – 1)2

SOLUTION:

ANSWER: 75

11. c2 + b

2

SOLUTION:

ANSWER: 28.25

12. 4c –7 + b3

SOLUTION:

ANSWER: –57



11 • 11 • 11 • 11 = 114

ANSWER:

114

14. 3 • 3 • 3 • 3 • 3


3 • 3 • 3 • 3 • 3 = 35

ANSWER:

35

15. (–8)(–8)(–8)(–8)(–8)(–8)


(–8)(–8)(–8)(–8)(–8)(–8) = (–8)6

ANSWER:

(–8)6

16. (–14) • (–14) • (–14)


(–14) • (–14) • (–14) = (–14)3

ANSWER:

(–14)3

17.

SOLUTION:


is 4.

ANSWER:

18. (–1.5)(–1.5)(–1.5)


(–1.5)(–1.5)(–1.5)= (–1.5)3

ANSWER:

(–1.5)3

19. ab • ab • ab • ab



4b

4

ANSWER:

(ab)4

or a

4b

4

20. 5 • p • p • p • q • q • q

SOLUTION:

ANSWER:

5p3q

3

21. 3 • 7 • m • m • n • n • n • n

SOLUTION:

ANSWER:

21m2n

4

22. 8(c + 4)(c + 4)


8(c + 4)(c + 4)= 8(c + 4)2

ANSWER:

8(c + 4)2

23. (n – 5)(n – 5)(n – 5)


(n – 5)(n – 5)(n – 5)= (n – 5)3

ANSWER:

(n – 5)3

24. (2x + 3y)(2x + 3y)


(2x + 3y)(2x + 3y)= (2x + 3y)2

ANSWER:

(2x + 3y)2





SOLUTION: a.





26 • 4

3 • 10


water is this?

SOLUTION:


ANSWER: 409,600 gal


27. y4

SOLUTION:

ANSWER: 81

28. z3

SOLUTION:

ANSWER: 15.625

29. 7x2

SOLUTION:

ANSWER: 28

30. xy3

SOLUTION:

ANSWER: –54

31. z2 + x

SOLUTION:

ANSWER: 4.25

32. y4

+ 9

SOLUTION:

ANSWER: 90

33. 2y + z3

SOLUTION:

ANSWER: 21.625

34. x2 + 2y – 3

SOLUTION:

ANSWER: 7

35. y2 – 3x + 8

SOLUTION:

ANSWER: 23

36. 4(y + 1)4

SOLUTION:

ANSWER: 1024

37. 3(2z + 4)2

SOLUTION:

ANSWER: 243

38. 5(x3 + 6)

SOLUTION:

ANSWER: –10



SOLUTION: a.


64,000 ft2.


63,000 ft2.


36,400 ft2.

b. 36,400 ft2 < 63,000 ft

2 < 64,000 ft

2


2 = 1000

ft2.

ANSWER:

a. 64,000 ft2; 63,000 ft

2; 36,400 ft

2

b. 36,400 ft2; 63,000 ft

2;64,000 ft

2

c. 1000 ft2


40. 92

SOLUTION:

ANSWER: 81

41. 113

SOLUTION:

ANSWER: 1331

42.

SOLUTION:

ANSWER:

43. (–5)4

SOLUTION:

ANSWER: 625

44. (–2)7

SOLUTION:

ANSWER: –128

45. 2 • 44

SOLUTION:

ANSWER: 512

46. 63 • 4

SOLUTION:

ANSWER: 864

47. 35 • 10

SOLUTION:

ANSWER: 2430

48. 22 • 10

SOLUTION:

ANSWER: 40

49. 73 • 2

2

SOLUTION:

ANSWER: 1372

50. 5 • 24

SOLUTION:

ANSWER: 80

51. (4.5)4 • 2

SOLUTION:

ANSWER: 820.125


52. 25 _ 52

SOLUTION:

32 > 25 so 25 > 5

2.

ANSWER: >

53. 36 _ 63

SOLUTION:

729 > 216 so 36 > 6

3.

ANSWER: >

54. 26 _ 82

SOLUTION:

64 = 64 so 26 = 8

2.

ANSWER: =

55. 83 _ 4

5

SOLUTION:

512 < 1024 so 83 < 4

5.

ANSWER: <

56. (–6)4 _ 64

SOLUTION:

1296 = 1296 so (–6)4 = 6

4.

ANSWER: =

57. (–4)6 _ (–4)

7

SOLUTION:

4096 > –16,384 so (–4)6 > (–4)

7.

ANSWER: >


SOLUTION: a.

b.


Side Length (cm)

Volume

(cm3)

1

2

4

8

16


ANSWER:

a. V = s3

b.



V = 8s3.


SOLUTION:




2304 mi

ANSWER:






SOLUTION:




ANSWER:





closer to 107 or 10

8? Explain.

SOLUTION:


7 =

10,000,000 and 108 = 100,000,000. 100,000,000 is


ANSWER:


7 =10,000,000 and 10

8 =




reasoning.

54 = 625

53 = 125

52 = 25

51 = 5



1.

54 = 625

53 = 125= 625÷5

52 = 25 = 125÷5

51 = 5 = 25÷5

50 = 1 = 5÷5

ANSWER:



1.






A 210

B 215

C 220

D 230


210


ANSWER: A


SOLUTION:




3 •2

3 = 8 • 8 • 8 = 512 acres.


0 = 1

8 21 = 2

16 22 = 4

24 23 = 8

ANSWER: 512


?

F 12 • 25

G 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2H 4 • 4 • 4 • 5 • 5

J 4 • 4 • 4 • 5 • 5 • 5

SOLUTION:


ANSWER: H

67. Evaluate .

A

B

C

D

SOLUTION:


ANSWER: B


SOLUTION: –12 + (–7) = –19

ANSWER: –19

69. 25 – (–5)

SOLUTION:

ANSWER: 30

70. –15 + 8

SOLUTION: –15 + 8 = –7

ANSWER: –7

71. –9 – (–9)

SOLUTION:

ANSWER: 0

72. 3 + (–11)

SOLUTION: 3 + (–11) = –8

ANSWER: –8

73. –18 – 2

SOLUTION:

ANSWER: –20




75. 19 × 5 = 5 × 19



76. 12 • 0 = 0





SOLUTION:


years.

ANSWER:

in.




ANSWER: 50 + 8d; $170





80. a profit of $75




81. 8 and 12


ANSWER: 4

82. 18 and 24


ANSWER: 6

83. 12 and 14


ANSWER: 2

84. 27 and 36


ANSWER: 9

85. 57 and 63


ANSWER: 3

86. 45 and 80


ANSWER: 5



ANSWER: 4

88. 60 ÷ (–4)


ANSWER: –15

89. –56 ÷ 8


ANSWER: –7

90. –81 ÷ (–3)


ANSWER: 27



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