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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
7-30 Holt McDougal Algebra 1
Review for Mastery
Division Properties of Exponents
The Quotient of Powers Property can be used to divide terms with exponents. m
n
a
a
= am – n (a 0, m and n are integers.)
Simplify 5
2
7.
7 Simplify
7
3.
x y
x
5
2
7
7 =
5 – 27
7
3
x y
x = x7 – 3 • y
= 73 = x4y
The Positive Power of a Quotient Property can be used to raise quotients to positive
powers. n
a
b =
n
n
a
b(a 0, b 0, n is a positive integer.)
Simplify
4
2.
5 Simplify
2x5
y4
3
.
4
2
5 =
4
4
2
5
35
4
2x
y =
5 3
4 3
(2 )
( )
x
y
= 16
625
=
3 5 3
4 3
2 ( )
( )
x
y
=
15
12
8x
y
Simplify.
1. 6
4
5
5 2.
6 5
3
x y
y 3.
( )
2 4
3
a b
ab
________________________ ________________________ ________________________
4.
3
2
5 5.
63
2
x
y 6.
23
2
3m
n
________________________ ________________________ ________________________
7.
3
2
a
b 8.
23x
xy 9.
2
30
20
________________________ ________________________ ________________________
LESSON
7-4
Use the Positive Power of a
Quotient Property.
Simplify.
Use the Positive
Power of a Quotient
Property.
Use the Power of a
Product Property.
Simplify.
Name _______________________________________ Date___________________ Class __________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
7-31 Holt McDougal Algebra 1
Review for Mastery
Division Properties of Exponents continued
You can divide quotients raised to a negative power by using the
Negative Power of a Quotient Property. –n
a
b=
n
b
a=
n
n
b
a (a 0, b 0, n is a positive integer)
Simplify
–2
3.
4 Simplify
–34
2
3.
a
b
–2
3
4 =
2
4
3
–34
2
3a
b =
32
43
b
a
=
2
2
4
3 =
2 3
4 3
( )
(3 )
b
a
= 16
9
=
2 3
3 4 33
b
a
i
i
=
6
1227
b
a
Fill in the blanks below.
10.
–3
3
5 =
3
11.
–53
7
xy
z =
5
12.
–42 3a b
c =
4
=
3
3 =
5
5 5
z
x y
i
i i
=
4
4 4
c
a b
i
i i
= = z
x y =
c
a b
Simplify.
13.
–5
x
y 14.
–2
4
7
3m 15.
–52
3
2a
b
________________________ ________________________ ________________________
16.
2
3
m
n 17.
–3
2
2
3x 18.
–4
32
r
s
________________________ ________________________ ________________________
LESSON
7-4
Rewrite with a positive
exponent.
Use the Positive Power
of a Quotient Property.
Simplify.
Rewrite with a
positive exponent.
Use the Positive
Power of a Quotient
Property.
Use the Power of a
Power Property.
Simplify.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A5 Holt McDougal Algebra 1
5. D 6. H
7. B 8. J
Reading Strategies
1. multiply 2. add
3. Power of a Product
4. Power of a Product; with both properties,
a number is applied to all parts.
5. m24 6. 88
7. 9v10 8. 8
5
d
c
9. 5832 10. 16y14
LESSON 7–4
Practice A
1. 4; 81 2. 8; 5; 3
3. 2; 7; 5; 5
1
t 4. 6; 3; 6; 4;
4
3
t
s
5. 13 4
1
a b 6.
5
1
xy
7.
64
9 8.
4
4
2
3; 16
81
9. 3
34
x;
3
64
x 10.
5
4; 25
16
11.
81a4
b4
256c8
12. 3
3
27
8
c
b
13. 2
3
4
3
x y
z;
8 4
12
256
81
x y
z 14.
4
n; 3
6
n; 2n
15. 1.5; 8
16. 0.2; 2; 2; 1; 2; 2 101
17. a. 3.5 101
b. $250,000
Practice B
1. 2; 36 2. 12; 7; t5
3. w7 4. 6
1
j
5. 5m3 6. 3
c
d
7. 7
1
x
8. 4
6
s
t
9. 27
8 10.
4
4
16
81
b
a
11. 4
4
81v
t 12.
2
2
49
16
t
s
13. 2
32
3cd 14.
4 481
16
m n
15. 2 1011 16. 5 106
17. 300,000 yards
18. 2.16 107 dresses
Practice C
1. 62 or 36 2. h7
3. 32
5 4.
4x
y
5. 2
8
n
mp 6.
2c
a
7. 49
16 8.
4
6
s
t
9. 5 5
57776
a b
c 10.
6 8
4 2
4d f
b c
11. 5 5 10
5
x y z
w 12.
44
1
10
13. 4 104 14. 9 108
15. 4 1010 16. 8 10 9
17. 4 18. 7
19. 3
20. $20,000 per minute
Review for Mastery
1. 25 2. x6 y2
3. b
a 4.
3
3
2
5 or
8
125
5. 18
12
x
y 6.
6
4
9m
n
7. 3
6
a
b 8.
4
2
x
y
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A6 Holt McDougal Algebra 1
9. 9
4 10.
5
3; 5
3; 125
27
11. 7
3
z
xy; 7; 1; 3; 35; 5; 15
12. 2 3
c
a b; 1; 2; 3; 4; 8; 12
13. 5
5
y
x 14.
89
49
m
15. 15
1032
b
a 16.
2
2
9n
m
17. 6
27
8
x 18.
12
4
16s
r
Challenge
1. 23 31 2. 22 33
3. 22 1131 4. 23 32 52
5. 2
3
2 • 3
2 • 3 =
2
3
2
6. 4
2 2
2 • 3
2 • 3 • 5 =
22
3 • 5
7. 3
5 2
2 • 5
2 • 3 =
3
4 2
5
2 • 3
8. 2 3
3 2 2
2 • 3 • 5
2 • 3 • 5 =
3
2 • 5
9. If a prime number base b appear in the
numerator (or denominator), it cannot
occur in the denominator (or numerator)
as well because then the rational number
is not fully simplified.
ex: n
m
b a
b c =
n mb a
c
10. Every rational number can be written as
a quotient whose numerator is 1 or the
product of prime numbers raised to
positive integer exponents and whose
denominator can be written as 1 or the
product of prime numbers raised to
positive integer exponents, and there
are no prime bases common to the
numerator and the denominator.
Problem Solving
1. 0.056 acres 2. 6y2 meters
3. 5.34 102 km/h
4. Laos: $1817; Norway: $39,869
5. C 6. F
7. C 8. H
Reading Strategies
1. subtract 2.
4
8
5
3. Positive Power of a Quotient
4. 144 5. 16
625
6. 64
81 7.
3
4 5
g
f h
8. 18
6
t
s 9.
10 5
32
c d
10. 8
27 11.
4
4
x
y
12. 14
625
g
f
LESSON 7–5
Practice A
1. B 2. D
3. C 4. A
5. 7 6. 3
7. 1 8. 12
9. 8 10. 9
11. 1 12. 32
13. x8 14. x3y4
15. m4n 16. x2
17. 14 cm
Practice B
1. 3 2. 11
3. 0 4. 11
5. 4 6. 8
