Lesson 16.1 Skills Practice Name_________________________________________________________ Date__________________________
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
© 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
10. (13x)2
11. (222y)4
12. 2(71y)5
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Lesson 16.1 Skills Practice
page 2
Write each power in expanded notation and evaluate to calculate the product. 13. 4 3
14. 2 4
The expanded notation is (4)(4)(4) 5 64.
15. 5 4
16. 7 5
17. 3 8
18. 63
Write each power in expanded notation and evaluate to calculate the product. 19. (28)3
20. (24)5
The expanded notation is
21. (23)4
22. (26)6
23. 2(25)
24. 2(56)
25. 2(72)
26. 2(83)
© Carnegie Learning
(28)(28)(28) 5 2512.
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Lesson 16.1 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 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. 3 2 x3
36. 2 5y2
The expanded notation is
© Carnegie Learning
(3)(3)(x)(x)(x).
37. 5 2 y4
38. x 5 z2
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Lesson 16.1 Skills Practice
page 4
39. (5x)4
40. (7x)2
41. (6z)3
42. (2xy)5
43. 5x3
44. 4y5
Write each expression in expanded notation. 45. 2(7z)5
46. 2(6y)3
The expanded notation is
47. (24a)3
48. (22b)6
49. 28z4
50. 26m7
51. 2(3x)2 y4
52. (28y)3 z2
© Carnegie Learning
2(7z)(7z)(7z)(7z)(7z).
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Lesson 16.1 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Write each expression using exponents. 53. (7)(7)(7)(7)
54. 2 2 2 2 2 2 2 2
The power is 7 . 4
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
The power is y .
© Carnegie Learning
5
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 16.1 Skills Practice
page 6
Write each expression using exponents. 73. (2x)(2x)(2x)(2y)(2y)
74. (2a)(2a)(2a)(2a)(c)(c)(c)(c)(c)
The power is (2x)3(2y)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
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
© Carnegie Learning
The power is (3x)3y3z5 .
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Lesson 16.2 Skills Practice Name_________________________________________________________ Date__________________________
Digital Storage Multiplying and Dividing Powers
Problem Set Write each expression in expanded form. 1. 5 2 54
2. 3 4 35
555555
3. 7 3 75
4. 2 2 23
Simplify each expression. Show your work. 5. (9)2(9)4
6. (24)3(24)7
(9)2(9)4 5 92 14
5 96
7. (22)2(22)5
8. (28)4(28)5
© Carnegie Learning
Write each expression in expanded form. 9. x 2 x3
10. y y2
xxxxx
11. m5 m2
12. n 4 n5
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Lesson 16.2 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
15. (2c)(2c)3
16. (2z)6(2z)2
Simplify each expression. Show your work. 17. x 2y2x3y5
18. a 3 b2ab4
x2y2x3y5 5 (x2x3)( y2y5)
5 x2 13 y2 15
5 x5 y7
20. 3mn3 8m6n7 © Carnegie Learning
19. 7y3z4 2yz3
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Lesson 16.2 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 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
© Carnegie Learning
21. 5y3 3yz3 z2
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Lesson 16.2 Skills Practice
page 4
Simplify each expression. Show your work. 28. (43)5
27. (22)3 (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. 34. ( y3)2
33. (x5)2 (x5)2 5 x5?2
35. (m3)5
36. (n4)3
37. (2b2)6
38. 2(m2)4
© Carnegie Learning
5 x10
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Lesson 16.2 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Simplify each expression. Show your work. 39. (3x2y)4
40. (2a2b3)5
(3x2y)4 5 34 (x2)4 y4
5 81(x)24y4
5 81x8y4
42. (25y3z2)5
43. (22cd2)4
44. (22x3y4 )2
© Carnegie Learning
41. (24mn3)3
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Lesson 16.2 Skills Practice
page 6
Write each numerator and denominator in expanded form. 4 45. __ 72 7
8 46. __ 45 4
? 7 __________ 7 ? 7 ? 7 7?7
96 47. __ 2 9
9 48. __ 53 5
Simplify each expression. Show your work. 68 50. __ 65
5 49. __ 32 3
__ 3522 32 5 5
3
5 33 9 52. ____ 3 2 23
Write each numerator and denominator in expanded form. 5 y4 53. __ x3 54. __ 3 x y x ? x ? x ? x _____________ ? x x?x?x
z7 55. __ 2 z
6 56. __ a3 a
© Carnegie Learning
2128 51. _____ 4 12
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Lesson 16.2 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ Simplify each expression. Show your work. n5 57. __ 4 n
m9 58. ___ 6 m
5 __ n 5 n524
4 n
© Carnegie Learning
5 n
b6 59. ____ 4 2b
2h14 60. _____ 6 h
212x7 61. ______ 2 3x
24y8 62. ____ 4 4y
45a7b3 63. ______ 4 25a b
10m8n3 64. _______ 2m7
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Lesson 16.2 Skills Practice
page 8
Simplify each expression. Show your work. 65. 3a2 4a3
66. 25m8 7m2
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. _____ 3 2g
5 72. _____ 14h4 2h
© Carnegie Learning
5 12a5
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Lesson 16.2 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ 40a5b7 74. _______ 28a2b6
218m5 m2 n4 _____________ 75. 26m3 n
56xy3 (x3y)2 y 76. ______________ 8x6 y
© Carnegie Learning
232x8y5 ________ 73. 4x6y
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© Carnegie Learning
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Lesson 16.3 Skills Practice Name_________________________________________________________ Date__________________________
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. 3 1. __ 53 5
4 2. __ 24 2
__ 53 5 5323 3
5
5 50 5 1
3. __ 7 72
6 4. __ 36 3
5. __ 4 49
6. __ 6 62
© Carnegie Learning
2
9
2
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Lesson 16.3 Skills Practice
page 2
Simplify each expression using the Quotient Rule of Powers. 7. __ 2 24 0
8. __ 9 95 0
__ 2024 24 5 0
2
5 224 9. __ 8 83
10. __ 4 43
50 11. __ 8 5
12. __ 3 32
0
0
0
Rewrite each expression so that the exponent is positive. 13. 3 22
14. 5 29
15. 6 23
16. 2 25
17. 4 28
18. 7 23
© Carnegie Learning
__ 1 32
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Lesson 16.3 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Rewrite each expression so that the exponent is positive. 19. x 23
20. y28
__ 1 x3
21. a 28 b22
22. m24 n25
23. y 24 z23
24. x 22 y26
Rewrite each expression so that the exponent is positive. 25. ___ 1 225
26. ___ 1 623
5 2 27. ___ 1 924
28. ___ 1 422
29. ___ 1 723
30. ___ 1 524
© Carnegie Learning
Rewrite each expression so that the exponent is positive. 31. ___ 1 y24
32. ___ 1 x27
y 4 33. ______ 1 x26y22
34. ______ 1 a23b28
35. _______ 1 m25 n29
36. _______ 1 g27 h24
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Lesson 16.3 Skills Practice
page 4
Simplify each expression. Show your work. 4 37. __ x4 x
y22 38. ___ 22 y
4 __ x424 x4 5
x
5 x0 5 1
40. (20)(25)
12x2y3 41. ______ 2 4x y
15a5b4 42. ______ 3a2b4
© Carnegie Learning
39. (60)(63)
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Lesson 16.3 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Simplify each expression. Then, calculate the value. Do not leave your answer as a power. 2 43. __ 34 3
5 44. __ 48 4
__ 3224 34 5 2
3
5 322 1 5 __ 32
© Carnegie Learning
1 5 __ 9
45. (65)(627)
46. (24)(228)
523 47. ___ 526
25 48. ___ 322 3
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Lesson 16.3 Skills Practice
page 6
Simplify each expression so that the exponent is positive. Show your work. y3 49. __ 5 y
50. __ x x9 4
y __ 5 y325 3
y5
5 y22 1 5 __ y2
a25 51. ___ a2
3 2 54. _____ m5n6 mn
© Carnegie Learning
x4y23 53. _____ 2 xy
8 52. ___ c24 c
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Lesson 16.3 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ (x2y25) ? (xy) 55. ___________ x4y3
2 3 5 58. __________ 5c d4 ? c d 40c ? cd7
© Carnegie Learning
4 6 n 57. __________ 36m 2 3 4m n mn8
18a2b2 56. __________ 6ab3 ? ab24
Chapter 16 Skills Practice • 987
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© Carnegie Learning
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Lesson 16.4 Skills Practice Name_________________________________________________________ Date__________________________
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
© Carnegie Learning
n in a 3 10n
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Lesson 16.4 Skills Practice
page 2
Problem Set Write each number in scientific notation. Show your work. 1. 45,000,000
2. 3700
45,000,000 5 (4.5)(10,000,000) 5 (4.5)(107) The number written in scientific notation is 4.5 3 107.
3. 562,000
4. 92,400,000,000
© Carnegie Learning
5. There are over 29,000 grains of long-grain rice in a one-pound bag.
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Lesson 16.4 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 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.
© 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 16.4 Skills Practice
page 4
10. 3.7 3 108
11. 2.871 3 1011
12. 4.26 3 109
© Carnegie Learning
13. There are about 1 3 105strands of hair on the human head.
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Lesson 16.4 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 14. The population of Texas is about 2.4 3 107 people.
15. The population of California is about 3.7 3 107people.
© Carnegie Learning
16. The circumference of the Earth at the equator is about 4.008 3 107meters.
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Lesson 16.4 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
© Carnegie Learning
19. 0.00000000253
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Lesson 16.4 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 21. A grain of rice weighs about 0.025 grams.
© Carnegie Learning
22. The diameter of a red blood cell is about 0.00004 inches.
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Lesson 16.4 Skills Practice
page 8
23. A grain of salt weighs about 0.0000585 grams.
© Carnegie Learning
24. A credit card is about 0.0299 inches thick.
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Lesson 16.4 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ 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)
( )
5 (8.3)___ 1 105
5 (8.3)________ 1 100,000
5 (8.3)(0.00001)
(
)
The number written in standard notation is 0.000083.
28. 3.85 3 10212
© Carnegie Learning
27. 4.7 3 1023
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Lesson 16.4 Skills Practice
page 10
29. An oxygen atom has a radius of about 4.8 3 10211meters.
© Carnegie Learning
30. The diameter of a white blood cell is about 1 3 1025meters.
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Lesson 16.4 Skills Practice
page 11
Name_________________________________________________________ Date__________________________ 31. A nitrogen atom has a radius of about 5.6 3 10211meters.
© Carnegie Learning
32. The width of a human hair is about 1.8 3 1023centimeters.
Chapter 16 Skills Practice • 999
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© Carnegie Learning
1000 • Chapter 16 Skills Practice
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Lesson 16.5 Skills Practice Name_________________________________________________________ Date__________________________
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)
© Carnegie Learning
3. (8 3 106)(1 3 1023)
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Lesson 16.5 Skills Practice
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
© Carnegie Learning
to calculate the length.
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Lesson 16.5 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 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
© Carnegie Learning
calculate the length.
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Lesson 16.5 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)
( )( )
5 (4)(10522)
5 (4)(103)
5 4 3 103
© Carnegie Learning
5 (8 3 105) _________ 5 __ 8 ___ 10 2 102 (2 3 102)
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Lesson 16.5 Skills Practice
page 5
© Carnegie Learning
Name_________________________________________________________ Date__________________________ (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)
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Lesson 16.5 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
5 2.8 3 109
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) © Carnegie Learning
23. (2.90 3 1027)(4.860 3 1022)
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Lesson 16.5 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 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
© Carnegie Learning
calculate the number of footballs.
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Lesson 16.5 Skills Practice
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
© Carnegie Learning
Sand cat? Use scientific notation to calculate the difference in weight.
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Lesson 16.6 Skills Practice Name_________________________________________________________ Date__________________________
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
Rule
Property of
Property of
Multiplication
Multiplication
1. 4x5 6x2 y6 xy
4x5 6x2 y6 xy 5 (4 6)(x5 x2 x)( y6 y) Commutative Property of Multiplication
5 (24)(x51211 )( y611 ) Product Rule of Powers 5 24x8y7
Simplify Powers
© Carnegie Learning
2. 3a2 b3 7ab5 b2
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Lesson 16.6 Skills Practice
page 2
3. (4m2 n5)3
4. (23x7 y3)5
296m9 n2 6. _________ 8m2 n6
© Carnegie Learning
27y8 z5 5. _______ 4 2 23y z
1010 • Chapter 16 Skills Practice
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Lesson 16.6 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 7. 22x5y3 8x2y25 x29 y2
m n 8. _____________ 42m n6 5 6m n 4 2
© Carnegie Learning
5 3
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Lesson 16.6 Skills Practice
page 4
Choose which solution is correct. c.
b.
9. a. 3x 4x 5 (3 4)(x x ) 2
3
2 3
3x 4x 5 (3 4)(x x ) 2
3
2 3
3x2 4x35 (3 4)(x2x3)
5 (12)(x213)
5 (12)(x223)
5 (12)(x23 )
5 (12)(x5)
5 (12)(x21)
5 (12)(x6)
5 12x5
12 5 ___ x
5 12x6
The correct solution is a.
b.
25a 2a 6
3
25a 2a
25a6 2a3
3
5 (25 2)(a6a3 )
5 (25 2)(a6a3 )
5 (25 2)(a6a3 )
5 (210)(a623)
5 (210)(a63)
5 (210)(a613)
5 (210)(a3)
5 (210)(a18)
5 (210)(a9)
5 210a3
5 210a18
5 210a9
11. a.
( 4 )( m)
b.
( 4 )( m)
c.
( 4 )( m)
36 m 36m ___ ______ 5 ____
36m ___ 36 m ______ 5 ____
36 m 36m ___ ______ 5 ____
5 (9)(m1244)
5 (9)(m1224)
5 (9)(m1214)
5 (9)(m3)
5 (9)(m8)
5 (9)(m16)
5 9m3
5 9m8
5 9m16
12
4m 4
c. 6
12 4
12
4m 4
12 4
12
4m 4
12 4
© Carnegie Learning
10. a.
1012 • Chapter 16 Skills Practice
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Lesson 16.6 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 12. a.
b.
( 5 )( x)
60x2 ___ 60 x2 ____ 5 __ 5x8
8
60x ___ 60 x ____ 5 __
x 60 x 5 ( 60 5x ) ( 5 )(x )
( 5 )( x)
2
2
2
5x8
____ 8
8
2
___ __ 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 ___ 6 x
13. a.
b.
(5x ) 5 (5) (x ) 2 3
3
2 3
c.
(5x ) 5 (5) (x ) 2 3
3
2 3
(5x2)3 5 (5)3(x2)3 3
5 (125)(x23)
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.
(4y ) 5 (4) ( y ) 23 3
© Carnegie Learning
c.
3
23 3
(4y ) 5 (4) ( y ) 23 3
3
23 3
(4y23)3 5 (4)3( y23)3
5 (64)( y2313)
5 (64)( y233)
5 (64)( y2323)
5 (64)( y0)
5 (64)( y29)
5 (64)( y26)
5 (64)(1)
5 ___ 64 y9
64 5 ___ y6
5 64
Chapter 16 Skills Practice • 1013
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Lesson 16.6 Skills Practice
page 6
Simplify each expression. Show your work. 15. 12x4y3 3x2y25
2a7b22 16. 17a25b23
12x4y3 3x2y25 5 (12 3)(x4x2)( y3y25)
5 (36)(x412)( y31(25))
5 (36)(x6)( y22)
36x 6 5 _____ y2
18. (2a5b2c3)5
28m3 n5 19. _______ 7 2 14m n
35x8y6 20. ______ 5 3 7x y
© Carnegie Learning
17. (23x4y23)2
1014 • Chapter 16 Skills Practice
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Lesson 16.6 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 21. (2x5y3)2 x2 y4
a b 22. ____________ 3a b7 4 6a b9
(4m3 n2)4 23. ________ 8m5
5x2 y4 6x4 y 24. __________ 10x3 y3
5
3
2
© Carnegie Learning
4
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© Carnegie Learning
1016 • Chapter 16 Skills Practice
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