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Lesson 13.1
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
Exponentially Speaking
Powers and Exponents
Vocabulary
Write the term that best completes each statement.
1. The
of a power is the number of times that the factor is repeatedly multiplied.
2. An expression used to represent a factor as repeated multiplication is called a
3. The
.
of a power is the repeated factor in a power.
Problem Set
State the base and the exponent of each power.
1. 94
2. 102
© 2011 Carnegie Learning
The base is 9 and the exponent is 4.
3. 186
4.
27
5. 2119
6.
2483
7. (215)2
8.
(214)6
9. 73x3
11. (222y)4
10. (13x)2
12. 2(71y)5
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Skills Practice
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Lesson 13.1
Skills Practice
page 2
Write each power in expanded notation and evaluate to calculate the product.
13. 43
14. 24
The expanded notation
is (4)(4)(4) 5 64.
15. 54
16. 75
17. 38
18. 63
Write each power in expanded notation and evaluate to calculate the product.
20. (24)5
19. (28)3
The expanded notation is
21. (23)4
22. (26)6
23. 2(25)
24. 2(56)
25. 2(72)
26. 2(83)
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Chapter 13
Skills Practice
© 2011 Carnegie Learning
(28)(28)(28) 5 2512.
Lesson 13.1
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
Write each expression in expanded notation and evaluate to calculate the product.
27. (4)2(25)3
28. (24)4(7)2
The expanded notation is
(4)(4)(25)(25)(25) 5 22000.
29. (2)5(26)2
30. (22)5(8)3
31. 2(3)6(2)4
32. 2(6)3(4)2
33. 2(4)3(8)2
34. 2(5)3(9)2
Write each expression in expanded notation.
35. 32x3
36. 25y2
© 2011 Carnegie Learning
The expanded notation is
(3)(3)(x)(x)(x).
37. 52y4
38. x5z2
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Lesson 13.1
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page 4
39. (5x)4
40. (7x)2
41. (6z)3
42. (2xy)5
43. 5x3
44. 4y5
Write each expression in expanded notation.
46. 2(6y)3
45. 2(7z)5
The expanded notation is
47. (24a)3
48. (22b)6
49. 28z4
50. 26m7
51. 2(3x)2 y4
52. (28y)3 z2
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Chapter 13
Skills Practice
© 2011 Carnegie Learning
2(7z)(7z)(7z)(7z)(7z).
Lesson 13.1
Skills Practice
page 5
1DPH________________________________________________________ 'DWH _________________________
Write each expression using exponents.
53. (7)(7)(7)(7)
54. 2 ? 2 ? 2 ? 2 ? 2 ? 2 ? 2 ? 2
The power is 74.
55. 4 ? 4 ? 4 ? 4 ? 4 ? 4
56. (5)(5)(5)(5)
57. (23)(23)(23)(23)(23)
58. 29 ? 29 ? 29 ? 29 ? 29 ? 29 ? 29
59. 24 ? 24 ? 24 ? 24 ? 24
60. 2(6)(6)(6)(6)
61. 22 ? 2 ? 2 ? 2 ? 2 ? 2 ? 2 ? 2
62. 25 ? 5 ? 5
Write each expression using exponents.
63. y ? y ? y ? y ? y
64. x ? x ? x ? x ? x ? x ? x ? x ? x
© 2011 Carnegie Learning
The power is y5.
65. (a)(a)(a)(a)(a)(a)(a)
66. b ? b ? b ? b ? b ? b
67. 2z ? 2z ? 2z ? 2z
68. (2m)(2m)(2m)(2m)(2m)(2m)
69. 2b ? 2b ? 2b ? 2b ? 2b
70. 2n ? n ? n ? n ? n
71. 2(x)(x)(x)(x)
72. 2y ? y ? y ? y ? y ? y ? y ? y
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Lesson 13.1
Skills Practice
page 6
Write each expression using exponents.
74. (2a)(2a)(2a)(2a)(c)(c)(c)(c)(c)
73. (2x)(2x)(2x)(2y)(2y)
The power is (2x) (2y) .
3
2
75. (2y) ? (2y) ? z ? z ? z ? z ? z
76. (2m) ? (2m) ? (2m) ? (2m) ? (2m) ? n ? n ? n
77. (2a)(2a)(2a)(b)(b)(b)
78. 26 ? 6 ? 6 ? b ? b ? h ? h ? h
79. 24 ? 4 ? 4 ? 4 ? 4 ? m ? m ? m ? n ? n
80. 23 ? 3 ? 3 ? 3 ? 3 ? y ? y ? y ? y ? z ? z ? z
81. 25 ? 5 ? a ? a ? a ? a ? a ? b ? b
82 . 22 ? 2 ? 2 ? 2 ? x ? x ? x ? y ? y ? y ? y
Write each expression using exponents.
83. 3x ? 3x ? 3x ? y ? y ? y ? z ? z ? z ? z ? z
84. 4a ? 4a ? 2b ? 2b ? 2b ? c ? c ? c ? c
The power is (3x) y z .
85. 5mn ? 5mn ? 5mn ? 5mn ? l ? l ? l
86. (22x)(22x)(22x)( y)( y)(z)(z)(z)
87. a ? a ? a ? (24b) ? (24b) ? c ? c
88. 26m ? 6m ? 6m ? 6m ? n ? n ? n
89. 23x ? 3x ? 3x ? (22y) ? (22y) ? z ? z ? z ? z
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3 3 5
Lesson 13.2
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
Digital Storage
Multiplying and Dividing Powers
Problem Set
Write each expression in expanded form.
2. 34 ? 35
1. 52 ? 54
5?5?5?5?5?5
3. 73 ? 75
4. 22 ? 23
Simplify each expression. Show your work.
5. (9)2(9)4
6. (24)3(24)7
(9)2(9)4 5 9214
5 96
© 2011 Carnegie Learning
7. (22)2(22)5
8. (28)4(28)5
Write each expression in expanded form.
9. x2 ? x3
10. y ? y2
x?x?x?x?x
11. m5 ? m2
12. n4 ? n5
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Lesson 13.2
Skills Practice
page 2
Simplify each expression. Show your work.
13. (2a)3(2a)4
14. (2b)2(2b)4
(2a)3(2a)4 5 (2a)314
5 (2a)7
16. (2z)6(2z)2
15. (2c)(2c)3
Simplify each expression. Show your work.
18. a3b2ab4
17. x2y2x3y5
x2y2x3y5 5 (x2x3)( y2y5)
5 x213y215
20. 3mn3 ? 8m6n7
19. 7y3z4 ? 2yz3
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5 x5y7
Lesson 13.2
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
22. 9b2 ? 2a5 ? a2b6
23. (2y)2 ? (2y)4 ? z ? z
24. (2m)2 ? n3 ? (2m)4 ? n2
25. 3x3 ? 2x2 ? y3 ? y
26. (2b) ? 4a ? (2b)5 ? 2a3
© 2011 Carnegie Learning
21. 5y3 ? 3yz3 ? z2
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Lesson 13.2
Skills Practice
page 4
Simplify each expression. Show your work.
27. (22)3
28. (43)5
(22)3 5 22?3
5 26
29. (72)4
30. (33)2
31. 2(22)4
32. 2(65)2
Simplify each expression. Show your work.
33. (x5)2
34. ( y3)2
(x5)2 5 x5?2
35. (m3)5
36. (n4)3
37. (2b2)6
38. 2(m2)4
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5 x10
Lesson 13.2
Skills Practice
page 5
1DPH________________________________________________________ 'DWH _________________________
Simplify each expression. Show your work.
39. (3x2y)4
40. (2a2b3)5
(3x2y)4 5 34(x2)4y4
5 81(x)2?4y4
5 81x8y4
42. (25y3z2)5
43. (22cd2)4
44. (22x3y4)2
© 2011 Carnegie Learning
41. (24mn3)3
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Lesson 13.2
Skills Practice
page 6
Write each numerator and denominator in expanded form.
74
45. __
72
48
46. __
45
7?7?7?7
__________
7?7
96
47. __2
9
59
48. __
53
Simplify each expression. Show your work.
68
50. __
65
35
49. __
32
5
3 5 3522
__
2
3
5 33
Write each numerator and denominator in expanded form.
y4
x5
53. __
54. __3
3
x
y
x?x?x?x?x
_____________
x?x?x
z7
55. __2
z
880
a6
56. __
a3
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Chapter 13
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© 2011 Carnegie Learning
39
52. ____
232
2128
51. _____
124
Lesson 13.2
Skills Practice
page 7
1DPH________________________________________________________ 'DWH _________________________
Simplify each expression. Show your work.
n5
57. __4
n
m9
58. ___6
m
n5 5 n524
__
n4
© 2011 Carnegie Learning
5n
b6
59. ____4
2b
2h14
60. _____
h6
212x7
61. ______
3x2
24y8
62. ____
4y4
45a7b3
63. ______
25a4b
10m8n3
64. _______
2m7
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Lesson 13.2
Skills Practice
page 8
Simplify each expression. Show your work.
66. 25m8 ? 7m2
65. 3a2 ? 4a3
3a2 ? 4a3 5 (3 ? 4)(a2 ? a3)
5 (12)(a213)
67. (22b)3 ? 3b4
68. (2n2)4
69. (25mn3)2
70. (4y3)2 ? (23y)2
12g5
71. _____
2g3
14h5
72. _____
2h4
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© 2011 Carnegie Learning
5 12a5
Lesson 13.2
Skills Practice
page 9
1DPH________________________________________________________ 'DWH _________________________
40a5b7
74. _______
28a2b6
218m5 ? m2n4
75. _____________
26m3n
56xy3 ? (x3y)2 ? y
76. ______________
8x6y
© 2011 Carnegie Learning
232x8y5
73. ________
4x6y
Chapter 13
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© 2011 Carnegie Learning
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Chapter 13
Skills Practice
Lesson 13.3
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
Extending the Rules
Zero and Negative Exponents
Problem Set
Simplify each expression using the properties of powers. Express your solution in expanded notation,
and then calculate the value.
53
1. __
53
24
2. __
24
3
5 5 5323
__
3
5
5 50
© 2011 Carnegie Learning
51
72
3. __
72
36
4. __
36
49
5. __
49
62
6. __
62
Chapter 13
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Lesson 13.3
Skills Practice
page 2
Simplify each expression using the Quotient Rule of Powers.
90
8. __
95
20
7. __
24
0
2 5 2024
__
4
2
5 224
80
9. __
83
40
10. __
43
50
11. __8
5
30
12. __
32
Rewrite each expression so that the exponent is positive.
14. 529
13. 322
15. 623
16. 225
17. 428
18. 723
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1
__
32
Lesson 13.3
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
Rewrite each expression so that the exponent is positive.
19. x23
20. y28
1
__
x3
21. a28b22
22. m24n25
23. y24z23
24. x22y26
Rewrite each expression so that the exponent is positive.
1
25. ___
225
1
26. ___
623
25
1
27. ___
924
1
28. ___
422
1
29. ___
723
1
30. ___
524
© 2011 Carnegie Learning
Rewrite each expression so that the exponent is positive.
1
31. ___
y24
1
32. ___
x27
y4
1
33. ______
x26y22
1
34. ______
a23b28
1
35. _______
m25 n29
1
36. _______
g27 h24
Chapter 13
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Lesson 13.3
Skills Practice
page 4
Simplify each expression. Show your work.
y22
38. ___
y22
x4
37. __
x4
x4 5 x424
__
4
x
5 x0
51
40. (20)(25)
12x2y3
41. ______
4x2y
15a5b4
42. ______
3a2b4
© 2011 Carnegie Learning
39. (60)(63)
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Lesson 13.3
Skills Practice
page 5
1DPH________________________________________________________ 'DWH _________________________
Simplify each expression. Then, calculate the value. Do not leave your answer as a power.
32
43. __
34
45
44. __
48
2
3 5 3224
__
4
3
5 322
1
5 __
32
© 2011 Carnegie Learning
1
5 __
9
45. (65)(627)
46. (24)(228)
523
47. ___
526
325
48. ___
322
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Lesson 13.3
Skills Practice
page 6
Simplify each expression so that the exponent is positive. Show your work.
y3
49. __5
y
x4
50. __
x9
3
y
__
5 y325
5
y
5 y22
1
5 __
y2
c8
52. ___
c24
a25
51. ___
a2
x4y23
53. _____
xy2
© 2011 Carnegie Learning
m3n2
54. _____
m5n6
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Lesson 13.3
Skills Practice
page 7
1DPH________________________________________________________ 'DWH _________________________
(x2y25) ? (xy)
55. ___________
x4y3
5c2d3 ? c5d
58. __________
40c4 ? cd7
© 2011 Carnegie Learning
36m4n6
57. __________
4m2n3 ? mn8
18a2b2
56. __________
6ab3 ? ab24
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© 2011 Carnegie Learning
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Chapter 13
Skills Practice
Lesson 13.4
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
Let’s Get Scientific!
Scientific Notation
Vocabulary
Match each definition to its corresponding term.
1. a way to express a very large or very
a. scientific notation
small number as the product of a number
between 1 and 10 and a power of 10
2. the decimal part of a number written in
scientific notation; the number a in a 3 10
3. an estimate of size expressed as a
b. order of magnitude
n
c. mantissa
power of 10
4. the exponent of 10 for a number written
d. characteristic
in scientific notation; the number
© 2011 Carnegie Learning
n in a 3 10n
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Lesson 13.4
Skills Practice
page 2
Problem Set
Write each number in scientific notation. Show your work.
2. 3700
1. 45,000,000
45,000,000 5 (4.5)(10,000,000)
5 (4.5)(107)
The number written in scientific notation is
4.5 3 107.
4. 92,400,000,000
3. 562,000
© 2011 Carnegie Learning
5. There are over 29,000 grains of long-grain rice in a one-pound bag.
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Lesson 13.4
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
6. There are about 100,000,000,000 stars in our galaxy.
7. The distance from the Earth to the Moon is about 385,000,000 meters.
© 2011 Carnegie Learning
8. The average distance between the Earth and the Sun is about 93,000,000 miles.
Write each number in standard notation. Show your work.
9. 5.2 3 107
5.2 3 107 5 (5.2)(107)
5 (5.2)(10,000,000)
The number written in standard notation is 52,000,000.
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Lesson 13.4
Skills Practice
page 4
10. 3.7 3 108
11. 2.871 3 1011
13. There are about 1 3 105 strands of hair on the human head.
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12. 4.26 3 109
Lesson 13.4
Skills Practice
page 5
1DPH________________________________________________________ 'DWH _________________________
14. The population of Texas is about 2.4 3 107 people.
15. The population of California is about 3.7 3 107 people.
© 2011 Carnegie Learning
16. The circumference of the Earth at the equator is about 4.008 3 107 meters.
Chapter 13
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Lesson 13.4
Skills Practice
page 6
Write each number in scientific notation. Show your work.
18. 0.000831
17. 0.000067
0.000067 5 (6.7)(0.00001)
1
0.00001 5 ________
100,000
1
5 ___
105
5 1025
The number written in scientific notation is
6.7 3 1025.
20. 0.00000092
© 2011 Carnegie Learning
19. 0.00000000253
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Lesson 13.4
Skills Practice
page 7
1DPH________________________________________________________ 'DWH _________________________
21. A grain of rice weighs about 0.025 grams.
© 2011 Carnegie Learning
22. The diameter of a red blood cell is about 0.00004 inches.
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Lesson 13.4
Skills Practice
page 8
23. A grain of salt weighs about 0.0000585 grams.
© 2011 Carnegie Learning
24. A credit card is about 0.0299 inches thick.
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Lesson 13.4
Skills Practice
page 9
1DPH________________________________________________________ 'DWH _________________________
Write each number in standard notation. Show your work.
25. 8.3 3 1025
26. 6.22 3 1029
8.3 3 1025 5 (8.3)(1025)
( )
1
5 (8.3) ___
105
(
)
1
5 (8.3) ________
100,000
5 (8.3)(0.00001)
The number written in standard notation is
0.000083.
28. 3.85 3 10212
© 2011 Carnegie Learning
27. 4.7 3 1023
Chapter 13
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Lesson 13.4
Skills Practice
page 10
29. An oxygen atom has a radius of about 4.8 3 10211 meters.
© 2011 Carnegie Learning
30. The diameter of a white blood cell is about 1 3 1025 meters.
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Lesson 13.4
Skills Practice
page 11
1DPH________________________________________________________ 'DWH _________________________
31. A nitrogen atom has a radius of about 5.6 3 10211 meters.
© 2011 Carnegie Learning
32. The width of a human hair is about 1.8 3 1023 centimeters.
Chapter 13
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© 2011 Carnegie Learning
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Chapter 13
Skills Practice
Lesson 13.5
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
Are We There Yet? What Is the Distance?
Operations with Scientific Notation
Problem Set
Calculate each product. Express the product in scientific notation.
2. (3 3 107)(2 3 105)
1. (4 3 103)(2 3 106)
(4 3 103)(2 3 106) 5 (4)(2)(103)(106)
5 (8)(10316)
5 8 3 109
4. (2 3 1023)(3 3 108)
5. (3.7 3 104)(5.2 3 109)
6. (7.9 3 103)(2.6 3 105)
© 2011 Carnegie Learning
3. (8 3 106)(1 3 1023)
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Lesson 13.5
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7. (2.8 3 1028)(6.31 3 104)
page 2
8. (4.2 3 1024)(9.1 3 1026)
9. Seismosaurus is the longest known dinosaur. It measured 1800 inches. How far would
3000 Seismosaurus dinosaurs span if they were placed head to tail? Use scientific notation
© 2011 Carnegie Learning
to calculate the length.
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Lesson 13.5
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
10. According to many scientists, Argentinosaurus is the heaviest known dinosaur. It weighed
220,000 pounds. How much would 1500 Argentinosaurus dinosaurs weigh? Use scientific
notation to calculate the weight.
11. The bee hummingbird is the world’s smallest bird. It is about 0.05842 meters long. How far would
2,000,000 bee hummingbirds span if they were placed head to tail? Use scientific notation to
© 2011 Carnegie Learning
calculate the length.
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Lesson 13.5
Skills Practice
page 4
12. The pygmy shrew is the world’s smallest mammal by weight. It weighs just 0.0013 kilograms.
How much would 3,000,000 pygmy shrews weigh? Use scientific notation to calculate the weight.
Simplify each expression. Express the quotient in scientific notation.
(8 3 105)
13. ________
(2 3 102)
(12 3 108)
14. __________
(6 3 103)
(8 3 10 )
8 ___
105
_________
5 __
5
(2 3 10 )
2
(2 )(10 )
2
5 (4)(10522)
© 2011 Carnegie Learning
5 (4)(103)
5 4 3 103
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Lesson 13.5
Skills Practice
page 5
© 2011 Carnegie Learning
1DPH________________________________________________________ 'DWH _________________________
(15 3 1027)
15. ___________
(5 3 104)
(18 3 1022)
16. ___________
(3 3 1026)
(1.508 3 107)
17. ____________
(2.6 3 103)
(5.92 3 106)
18. ___________
(3.7 3 104)
(3.68 3 1028)
19. ____________
(3.2 3 1024)
(8.82 3 1027)
20. ____________
(2.52 3 1022)
Chapter 13
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Lesson 13.5
Skills Practice
page 6
Simplify each expression. Express your answer in scientific notation.
21. (5.9 3 105)(4.8 3 103)
22. (7.83 3 103)(2.9 3 108)
(5.9 3 105)(4.8 3 103) 5 (5.9)(4.8)(105)(103)
5 (28.32)(10513)
5 28.32 3 108
23. (2.90 3 1027)(4.860 3 1022)
24. (5.31 3 105)(6 3 1028)
(4.5 3 105)
25. __________
(3.8 3 102)
(5.12 3 106)
26. ___________
(8 3 103)
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5 2.8 3 109
Lesson 13.5
Skills Practice
page 7
1DPH________________________________________________________ 'DWH _________________________
27. A football is about 280 millimeters long. A football field is about 100,000 millimeters long. How
many footballs placed end to end would be needed to span the field? Use scientific notation to
© 2011 Carnegie Learning
calculate the number of footballs.
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Lesson 13.5
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page 8
28. A large Siberian tiger can weigh up to 305,000 grams. A small Sand cat can weigh as little as
1500 grams. How many times greater is the weight of a Siberian tiger than the weight of a
© 2011 Carnegie Learning
Sand cat? Use scientific notation to calculate the difference in weight.
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Chapter 13
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Lesson 13.6
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
Watch Your Step!
Identifying the Properties of Powers
Problem Set
Justify each step to simplify the expression. Choose the properties from the box.
Product Rule
Power to a
Negative
Quotient Rule
of Powers
Power Rule
Exponent Rule
of Powers
Zero Power
Simplify Powers
Identity
Commutative
Property of
Property of
Multiplication
Multiplication
Rule
1. 4x5 ? 6x2y6 ? xy
4x5 ? 6x2y6 ? xy 5 (4 ? 6)(x5x2x)( y6y) Commutative Property of Multiplication
5 (24)(x51211)( y611)
Product Rule of Powers
5 24x8y7
Simplify Powers
© 2011 Carnegie Learning
2. 3a2b3 ? 7ab5 ? b2
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Lesson 13.6
Skills Practice
page 2
3. (4m2n5)3
4. (23x7y3)5
© 2011 Carnegie Learning
27y8z5
5. _______
23y4z2
296m9n2
6. _________
8m2n6
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Lesson 13.6
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
7. 22x5y3 ? 8x2y25 ? x29y2
© 2011 Carnegie Learning
42m5n3 ? m4n2
8. _____________
6m6n5
Chapter 13
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Lesson 13.6
Skills Practice
page 4
Choose which solution is correct.
c.
b.
9. a.
2
3
2 3
3x ? 4x 5 (3 ? 4)(x x )
2
3
2 3
3x ? 4x 5 (3 ? 4)(x x )
3x2 ? 4x3 5 (3 ? 4)(x2x3)
5 (12)(x213)
5 (12)(x223)
5 (12)(x2?3)
5 (12)(x5)
5 (12)(x21)
5 (12)(x6)
5 12x5
12
5 ___
x
5 12x6
The correct solution is a.
b.
6
25a ? 2a
3
25a ? 2a
3
25a6 ? 2a3
5 (25 ? 2)(a6 a3)
5 (25 ? 2)(a6 a3)
5 (25 ? 2)(a6 a3)
5 (210)(a623)
5 (210)(a6?3)
5 (210)(a613)
5 (210)(a3)
5 (210)(a18)
5 (210)(a9)
5 210a3
5 210a18
5 210a9
11. a.
b.
12
12
36 m
36m
______
5 ___ ____
4m
916
c.
6
•
4
( 4 )( m )
4
c.
12
12
36m
36 m
______
5 ___ ____
4m
4
( 4 )( m )
4
12
12
36 m
36m
______
5 ___ ____
4
4m
( 4 )( m )
4
5 (9)(m1244)
5 (9)(m1224)
5 (9)(m1214)
5 (9)(m3)
5 (9)(m8)
5 (9)(m16)
5 9m3
5 9m8
5 9m16
Chapter 13
Skills Practice
© 2011 Carnegie Learning
10. a.
Lesson 13.6
Skills Practice
page 5
1DPH________________________________________________________ 'DWH _________________________
12. a.
2
2
60x
60 x
____
5 ___ __
5x
2
8
( 5 )( x )
5x8
2
( 605xx ) 5 ( 605 )(xx )
2
60x
60 x
____
5 ___ __
( 5 )( x )
8
____
___ __
8
8
8
5 (12)(x822)
5 (12)(x218)
5 (12)(x228)
5 (12)(x6)
5 (12)(x10)
5 (12)(x26)
5 12x6
5 12x10
12
5 ___
x6
13. a.
b.
2 3
3
2 3
(5x ) 5 (5) (x )
c.
2 3
3
2 3
(5x ) 5 (5) (x )
(5x2)3 5 (5)3(x2)3
3
5 (125)(x2?3)
5 (125)(x213)
5 (125)(x2 )
5 (125)(x6)
5 (125)(x5)
5 (125)(x8)
5 125x6
5 125x5
5 125x8
14. a.
c.
b.
23 3
© 2011 Carnegie Learning
c.
b.
2
3
23 3
(4y ) 5 (4) ( y )
23 3
3
23 3
(4y ) 5 (4) ( y )
(4y23)3 5 (4)3( y23)3
5 (64)( y2313)
5 (64)( y23?3)
5 (64)( y2323)
5 (64)( y0)
5 (64)( y29)
5 (64)( y26)
5 (64)(1)
64
5 ___
y9
64
5 ___
y6
5 64
Chapter 13
Skills Practice
•
917
Lesson 13.6
Skills Practice
page 6
Simplify each expression. Show your work.
15. 12x4y3 ? 3x2y25
16. 17a25 b23 ? 2a7 b22
12x4y3 ? 3x2y25 5 (12 ? 3)(x4x2)( y3y25)
5 (36)(x412)( y31(25))
5 (36)(x6)( y22)
36x
5 _____
y2
6
18. (2a5b2c3)5
28m3n5
19. _______
14m7n2
35x8y6
20. ______
7x5y3
© 2011 Carnegie Learning
17. (23x4y23)2
918
•
Chapter 13
Skills Practice
Lesson 13.6
Skills Practice
page 7
1DPH________________________________________________________ 'DWH _________________________
3a4b5 ? 4a3b2
22. ____________
6a7b9
(4m3n2)4
23. ________
8m5
5x2y4 ? 6x4y
24. __________
10x3y3
© 2011 Carnegie Learning
21. (2x5y3)2 ? x2y4
Chapter 13
Skills Practice
•
919
© 2011 Carnegie Learning
920
•
Chapter 13
Skills Practice