8-5: Division Properties of Exponents

Objectives:1. To divide powers with the same base.2. To raise a quotient to a power.

Check Skills/Warm Ups

Write each fraction in simplest form.

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

Solutions

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

= = 5 20

5 • 15 • 4

14

12525

25 • 525 • 1= = 5

60 100

20 • 320 • 5

35= = 124

4 = = 314 • 314 • 1

6 15

25

3 • 23 • 5= = = = 8

30 2 • 4 2 • 15

4 15

1035

27

5 • 25 • 7= = 18

6327

9 • 29 • 7= =

5xy15x

y3

5 • x • y5 • 3 • x= =

6y2

3x2y2

x3 • 2 • y2

3 • x= =

3ac12a

3 • a • c3 • 4 • a

c4= = 24m

6mn2

6 • 4 • m6 • m • n2

4 n2= =

Questions??

Homework Solutions1. 4

2. 4

3. 0.1

4. 2.50

5. –0.25

6. 2

7. 40, 80, 160

8. 48, 96, 192

9. 20.25, 30.375,

45.5625

10. –0.5, 0.25, –

0.125

11. 0.36, 0.072,

0.0144

12. –48, 96, –192

13. geometric

14. arithmetic

15. geometric

16. arithmetic

17. arithmetic

18. geometric

19. 5; 135; 10,935

20. –5; –135; –10,935

21. 5; –135; –10,935

22. 0.5; 13.5, 1093.5

23. –2; –250; –156,250

Homework (cont.)24. –1.1; 70.4; 18,022.4

25. A(n) = 6 • 0.5n–1; 0.37

26. A(n) = –6 • 2n–1; –3072

27. A(n) = 7 • (1.1)n–1; 9.317

60.

61.

62.

63. 2.467 10–3

55. a4

56. 16

57.

58. 1

59.

1 x10z20

Questions??

8-5: Division Properties of Exponents

Objectives:1. To divide powers with the same base.2. To raise a quotient to a power.

Key Concepts*You can use repeated multiplication to simplify fractions. Expand the numerator and the denominator using repeated multiplication. Then cancel like terms. Like this:

*Since division by zero is undefined, assume that no variable is equal to zero.

Key Concepts (cont.)

*You can use repeated multiplication to simplify the expression

Simplify each expression.

x4

x9a.

Simplify the exponents.= x–5

Rewrite using positive exponents. 1 x5=

p3 j –4

p–3 j 6

= p6 j –10 Simplify.

Rewrite using positive exponents.p6

j10=

b.

=Subtract exponents when dividing powers with the same base.x4 – 9

= Subtract exponents when dividing powers with the same base.

p3 – (–3)j –4 – 6

Example 1:

A small dog’s heart beats about 64 million beats in a year. If there are

about 530 thousand minutes in a year, what is its average heart rate in

beats per minute?

64 million beats 530 thousand min

6.4 107 beats5.3 105 min

= Write in scientific notation.

6.45.3 107–5= Subtract exponents when dividing powers

with the same base.

6.45.3 102= Simplify the exponent.

1.21 102 Divide. Round to the nearest hundredth.

= 121 Write in standard notation.

The dog’s average heart rate is about 121 beats per minute.

Example 2:Oh No, A Word

Problem!!

Simplify 3 y 3

4

34

y 12= Multiply the exponent in the denominator.

81y 12= Simplify.

Example 3:

3 y 3

4 34

(y 3)4= Raise the numerator and the denominator to the fourth power.

(a.) Simplify23

–3

33

23= Raise the numerator and the denominator to the third power.

Simplify.278 3 3

8or=

Example 4:

23

–3 32

3= Rewrite using the reciprocal of

23

(b.) Simplify

Raise the numerator and denominator to the second power.

(–c)2

(4b)2=

Simplify.c2

16b2=

Example 4: (continued)

4bc

–

4bc

––2 c

4b–

2= Rewrite using the reciprocal of .4b

c–

Write the fraction with a negative numerator.

c 4b

– 2=

–2

Simplify each expression.

1. 2. 3.

4. 5. 6.

a8

a–2w3

w7

(3a)4(2a–2)6a2

1.6 103

4 10–224

5

4x 3

3x 2

a10 1 w4 27

4 104 25625 or 10 6

25

27 64x3

Try These:

2–3

Questions?

HW #41: p. 420 #2-36even, 43-46, 52, 53, 56, 59