Name ________________________________________ Date __________________ Class__________________
Practice B
LESSON
7-5
Rational Exponents
Simplify each expression. All variables represent nonnegative
numbers.
1.
4.
1
3
27
2.
10.
_________________________
1
2
64
1
4
16
+
1
3
27
5.
1
5
1
+
1
2
49
16.
1
3
+8
3
16 4
5
16
11.
y5
12.
x 4 y 12
_________________________
1
( x 2 )4
1
( x 3 y )3
x6
________________________
17.
x2y 2
3
32 5
3
1212
________________________
15.
________________________
−
1
6
64
________________________
_________________________
14.
1
2
100
________________________
9.
_________________________
5
6.
3
8. 25
2
________________________
1
3
0
________________________
_________________________
________________________
13.
3.
________________________
________________________
7.
1
2
121
3
a 6 b3
________________________
18.
_________________________
1
4
(x )8
3
x3
________________________
1
19. Given a cube with volume V, you can use the formula P = 4V 3 to find
the perimeter of one of the cube’s square faces. Find the perimeter of
a face of a cube that has volume 125 m3.
_________________________________________________________________________________________
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7-36
Holt McDougal Algebra 1
9.
9
4
10.
5 5 125
; ;
3 3 27
Problem Solving
1. 0.056 acres
z7
; 7; 1; 3; 35; 5; 15
11.
xy 3
12.
c
; 1; 2; 3; 4; 8; 12
a 2 b3
13.
y5
x5
14.
15
2. 6y 2 meters
3. 5.34 102 km/h
4. Laos: $1817; Norway: $39,869
9m 8
49
5. C
6. F
7. C
8. H
Reading Strategies
2
15.
b
32a10
16.
9n
m2
17.
27 x 6
8
18.
16s12
r4
1. subtract
8
2. 5
4
3. Positive Power of a Quotient
4. 144
5.
16
625
6.
64
81
7.
g3
f 4 h5
8.
t 18
s6
9.
32
c d5
24 • 3
22
=
6. 2 2
3•5
2 •3 •5
10.
8
27
11.
2 • 53
53
7. 5 2 = 4 2
2 •3
2 •3
12.
g 14
25f 6
Challenge
1. 23 31
2. 22 33
3. 22 1131
4. 23 32 52
3
2 • 32
5. 3
= 2
2 •3
2
8.
3
22 • 3 3 • 5
=
3
2
2
2•5
2 •3 •5
10
x4
y4
LESSON 7–5
Practice A
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.
bn a
bn ma
ex: m =
c
b 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.
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. x
8
15. m4n
14. x3y4
16. x2
17. 14 cm
Practice B
1. 3
2. 11
3. 0
4. 11
5. 4
6. 8
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A6
Holt McDougal Algebra 1
7. 8
Challenge
8. 125
9. 8
10. 8
11. 1
12. 1331
13. y
14. x2y6
15. a2b
16. x5
17. x2y4
18. x
19. 20 m
Practice C
1. 9
2. 6
3. 10
4. 15
5. 8
6. 3
7. −3
8. 1024
9. 27
10. 9
11. 16
12. 1728
13. x2
14. x8y
15. y3z4
16. ab5
17. x
18. y
2
19. 54 cm
Problem Solving
Review for Mastery
1. 6 s
1. 8
2. 10
3. 512 in
3. 1
4. 4
5. D
5. 2
6. 7
7. A
7. 6
8. 14
9. 3
10. 1
11. 7
12. 5
13. 8
14. 8
15. 4
16. 1
17. 81
18. 1000
19. 4
20. 243
21. 8
22. 32
23. 343
24. 256
2. 51.3 mi/h
3
4. 4 cm
6. G
Reading Strategies
1. 3rd or cube
2. 5th
3. 5th; 4th
4. 2
5. 9
6. 2
7. 20
8. 4
9. 27
10. 8
11. 1024
12. 64
LESSON 7–6
Practice A
1. 2; 1
2. 3; 2
3. 5; 4
4. trinomial
5. monomial
6. binomial
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A7
Holt McDougal Algebra 1