The Museum of Natural History Powers and Prime … · The Museum of Natural History Powers and...
Transcript of The Museum of Natural History Powers and Prime … · The Museum of Natural History Powers and...
Chapter 9 ● Skills Practice 611
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Skills Practice Skills Practice for Lesson 9.1
Name _____________________________________________ Date _________________________
The Museum of Natural HistoryPowers and Prime Factorization
Vocabulary
Define each term in your own words.
1. factor
2. prime number
3. composite number
4. prime factorization
Problem Set
Use the given information to answer each question.
1. There are 8 apples in a basket. Can they be evenly divided in three groups? Can they be
evenly divided in four groups?
No, 8 apples cannot be evenly divided in three groups. Yes, 8 apples can be evenly divided in four groups of 2.
2. There are 15 chocolates in a box. Can they be evenly split by five friends? Can they be
evenly split by four friends?
3. There are 16 girls and 12 boys in a classroom. Can they be evenly divided in four groups of
girls and boys?
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4. There are 18 girls and 20 boys in a classroom. Can they be evenly divided in four groups of
girls and boys?
For each pair of numbers, list all the factors of each number. Then write the common factors of the pair of numbers.
5. 9 and 27
9: 1, 3, 927: 1, 3, 9, 27
Common factors: 1, 3, 9
6. 4 and 32
7. 10 and 12
8. 20 and 15
9. 6 and 17
10. 13 and 8
11. 34 and 60
Chapter 9 ● Skills Practice 613
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12. 26 and 90
Identify which numbers are prime and which numbers are composite.
13. 2, 7, 12, 14
Prime numbers: 2, 7Composite numbers: 12, 14
14. 3, 5, 6, 10
15. 8, 11, 17, 21
16. 13, 15, 16, 19
17. 27, 32, 37
18. 22, 29, 33
Write the prime factorization of each number.
19. 15
15 � 3 � 5
20. 14
21. 12
22. 18
23. 33
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24. 34
25. 60
26. 42
Use prime factorization to write the common factors of each pair of numbers.
27. 16 and 28
16 � 24, 28 � 22 � 7
2, 22 � 4
The common factors are 2 and 4.
28. 30 and 12
29. 25 and 40
30. 15 and 27
31. 41 and 14
32. 13 and 32
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33. 36 and 24
34. 54 and 18
35. 60 and 90
36. 100 and 150
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Chapter 9 ● Skills Practice 617
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Skills Practice Skills Practice for Lesson 9.2
Name _____________________________________________ Date _________________________
Bits and BytesMultiplying and Dividing Powers
Vocabulary
Write the term that best completes each statement.
1. The expression 36 is an example of a(n) .
2. When 6 is divided by 2, the is 3.
3. The expression 52 is equivalent to the of 5 and 5.
4. The in the expression 43 is the number 3.
Problem Sets Write each expression as a power.
1. 3 � 3 � 3 � 3 � 3 � 3 � 3 2. 2 � 2 � 2 � 2 � 2
37
3. 31 � 31 4. 17 � 17 � 17
5. 5 � 5 � 5 � 5 � 5 � 5 � 23 � 23 6. 11 � 11 � 11 � 11 � 19 � 19 � 19
7. 2 � 2 � 2 � 2 � 37 � 37 8. 3 � 3 � 3 � 31 � 31 � 31
Write the prime factorization of each number.
9. 27 10. 32
33
11. 28 12. 18
13. 70 14. 66
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15. 128 16. 512
17. 100 18. 1000
Multiply the powers. Write your answer as a power.
19. 43 45 20. 102 103
43 � 45 � 43�5 � 48
21. 28 23 22. 35 39
23. 11 114 24. 93 9
25. 2315 238 26. 3147 3115
Divide the powers. Write your answer as a power.
27. 28
__ 23
28. 39
__ 32
28 __
23 � 28�3 � 25
29. 47
__ 44
30. 84
__ 83
31. 175
___ 174
32. 226
___ 223
33. 6752
____ 6724
34. 5347
____ 5329
Chapter 9 ● Skills Practice 619
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Simplify each expression, if possible. Write your answer as a power.
35. 1213 1216 36. 158 1533
1213 � 1216 � 1213�16 � 1229
37. 615 156 38. 212 313
39. 167
___ 162
40. 106
___ 102
41. 83
__ 38
42. 710
___ 57
43. 4228
____ 4215
44. 3352
____ 3333
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Skills Practice Skills Practice for Lesson 9.3
Name _____________________________________________ Date _________________________
As Time Goes ByZero and Negative Exponents
Vocabulary
Provide an example of each term below.
1. positive exponent 2. negative exponent
3. zero exponent
Problem Sets
Write each number using a power with a positive exponent.
1. 1,000,000 2. 100,000,000
106
3. 1 _____ 1000
4. 1 ____ 100
5. 1 _______ 10,000
6. 1 ________ 100,000
7. 1 ___ 49
8. 1 ___ 25
9. 1 ____ 121
10. 1 ___ 32
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Rewrite each power so that the exponent is positive.
11. 8�1 12. 2�3
1 __ 8
13. 5�8 14. 4�7
15. 6�17 16. 18�1
17. 23�2 18. 70�12
19. 500�25 20. 120�30
Rewrite each fraction so that there is no power in the denominator.
21. 1 __ 24
22. 1 __ 3
2�4
23. 1 ___ 202
24. 1 ___ 13
25. 1 __ 7 26. 1 __
64
27. 1 ____ 4011
28. 1 ____ 5620
29. 1 _____ 12850
30. 1 _____ 5769
Chapter 9 ● Skills Practice 623
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Simplify each expression completely.
31. 120 32. 190
� 1
33. 31�4 315 34. 675 67�5
35. 26 2�3 36. 5�4 57
37. 8�8 8 38. 133 13�5
39. 170 172 40. 21�3 210
41. 7�4 74 42. 16�5 165
43. 100
___ 104
44. 2�5
___ 20
45. 42
__ 45
46. 6 __ 63
47. 122
___ 122
48. 9�7
___ 9�7
49. 3�9
___ 35
50. 45
___ 4�3
51. 91�8
____ 91�9
52. 53�27
_____ 53�26
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Chapter 9 ● Skills Practice 625
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Skills Practice Skills Practice for Lesson 9.4
Name _____________________________________________ Date__________________________
Large and Small MeasurementsScientific Notation
Vocabulary Provide an example of each number described.
1. A very large number written in scientific notation
2. A very large number written in standard form
3. A very small number written in scientific notation
4. A very small number written in standard form
Problem Set Write each number in standard form.
1. 4.1 � 10 5 2. 9.9 � 10 8
410,000
3. 1.35 � 10 6 4. 8.06 � 10 7
5. 2.708 � 10 11 6. 5.001 � 10 4
7. 3.6954 � 10 9 8. 6.0049 � 10 10
Write each number using scientific notation.
9. 18,000 10. 121,000
1.8 � 10 4
11. 400,000 12. 3,980,000
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13. 20,900,000 14. 466,600,000
15. 5,500,500,000 16. 120,090,000,000
List each set of numbers in order from least to greatest.
17. 1.0 � 10 5 , 9.98 � 10 4 , 8.705 � 10 4
8.705 � 10 4 , 9.98 � 10 4 , 1.0 � 10 5
18. 8.8 � 10 3 , 8.68 � 10 3 , 5.0 � 10 4
19. 4.355 � 10 5 , 6.02 � 10 7 , 4.99 � 10 5 , 5.0 � 10 6
20. 2.3 � 10 8 , 3.2 � 10 7 , 3.23 � 10 8 , 2.332 � 10 7
21. 4.44 � 10 5 , 5.04 � 10 6 , 4.5 � 10 7 , 4.555 � 10 8
22. 6.01 � 10 11 , 8.675 � 10 9 , 5.08 � 10 10 , 8.0 � 10 10
23. 1.01 � 10 15 , 1.1 � 10 14 , 1.011 � 10 15 , 1.11 � 10 16 , 1.111 � 10 15
24. 2.61 � 10 12 , 3.1 � 10 13 , 6.44 � 10 13 , 3.645 � 10 11 , 3.008 � 10 12
Write each number in standard form.
25. 1.8 � 10 –4 26. 5.2 � 10 –6
0.00018
27. 9.09 � 10 –7 28. 4.11 � 10 –8
29. 3.001 � 10 –11 30. 8.753 � 10 –5
Chapter 9 ● Skills Practice 627
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31. 7.6182 � 10 –10 32. 5.2548 � 10 –9
Write each number using scientific notation.
33. 0.0007 34. 0.000061
7.0 � 10 –4
35. 0.0000604 36. 0.000005
37. 0.0000040576 38. 0.0000000314
39. 0.0000001124 40. 0.0000000090065
List each set of numbers in order from least to greatest.
41. 5.2 � 10 –3 , 7.815 � 10 –3 , 6.01 � 10 –2
5.2 � 10 –3 , 7.815 � 10 –3 , 6.01 � 10 –2
42. 4.678 � 10 –4 , 4.0 � 10 –5 , 4.67 � 10 –4
43. 1.055 � 10 –7 , 3.23 � 10 –8 , 4.12 � 10 –5 , 3.9 � 10 –6
44. 9.6 � 10 –5 , 4.1 � 10 –6 , 8.495 � 10 –5 , 2.95 � 10 –6
45. 7.88 � 10 –8 , 7.08 � 10 –9 , 8.8 � 10 –7 , 7.008 � 10 –9
46. 2.01 � 10 –11 , 1.202 � 10 –12 , 2.1 � 10 –12 , 1.2 � 10 –11
47. 6.34 � 10 –13 , 4.4 � 10 –12 , 7.043 � 10 –13 , 5.16 � 10 –14 , 4.826 � 10 –12
48. 7.2 � 10 –17 , 7.27 � 10 –17 , 7.7 � 10 –18 , 7.277 � 10 –18 , 7.227 � 10 –17
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Skills Practice Skills Practice for Lesson 9.5
Name _____________________________________________ Date _________________________
The Beat Goes OnProperties of Powers
Vocabulary Match each rule with the example that demonstrates it.
1. power of a power rule a. 22 23 � 22�3 � 25
2. product rule of powers b. ( 4 __ 3 )
3
� 43
__ 33
3. power of a product rule c. (204)5 � 204(5) � 2020
4. quotient rule of powers d. 52
__ 50
� 52�0 � 52
5. power of a quotient rule e. (5 3)4 � 54 34
Problem Set
Rewrite each expression using the Power to a Power Property.
1. (32)2 2. (23)2
� 32(2) � 34
3. (57)2 4. (64)3
5. (175)6 6. (1213)3
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Rewrite each expression using the Power of a Product Property.
7. (2 13)3 8. (14 5)4
� 23 � 133
9. (4 16)2 10. (8 10)5
11. (17 12)2 12. (21 9)3
13. (5 23)7 14. (31 4)6
Rewrite each expression using the Power of a Quotient Property.
15. ( 3 __ 5 )
8
16. ( 6 __ 7 )
4
� 38 __
58
17. ( 13 ___ 6 )
7
18. ( 16 ___ 3 )
3
19. ( 8 ___ 27
) 10
20. ( 9 ___ 22
) 15
21. ( 19 ___ 4 )
5
22. ( 37 ___ 2 )
9
Simplify each algebraic expression.
23. (y5)3 24. (y4)2
(y5)3 � y5(3) � y15
25. (5a)3 26. (12b)2
27. z13z8 28. z6z21
Chapter 9 ● Skills Practice 631
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29. ( x __ 8 )
5 30. ( 6 __ x )
11
31. k15
___ k22
32. k43
___ k29
For each problem below, identify the property that is used in each step to simplify the expression.
33. ( x�4x5y
______ 22y3
) 2
� ( xy ____
22y3 )
2
product rule of powers
� (xy)2
______ (22y3)2
power of a quotient
� x2y2
_______ (22)2(y3)2
power of a product
� x2y2
____ 24y6
power of a power
� x2
____ 24y4
quotient rule of powers
34. ( 104x _______ 103x2y2
) 3
� (104x)3
________ (103x2y2)3
� (104)3x3
____________ (103)3(x2)3(y2)3
� 1012x3
_______ 109x6y6
� 103
____ x3y6
35. 5a6a4
_____ (a2)3
(ab)2 � 5a10
____ (a2)3
(ab)2
� 5a10
____ a6
(ab)2
� 5a4 (ab)2
� 5a4 a2b2
� 5a6b2
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36. (a2)3 (ab)5
__________
b3
__ b2
�
(a2)3 (ab)5 __________
b
� a6 (ab)5
________ b
� a6 a5b5
________ b
� a11b5
_____ b
� a11b4
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Skills Practice Skills Practice for Lesson 9.6
Name _____________________________________________ Date _________________________
Sailing AwayRadicals and Rational Exponents
Vocabulary Match each definition to its corresponding term.
1. The quantity under a radical sign in an expression a. cube root
2. A number b such that b n � a, where a is a number b. index
and n is a positive number
3. An expression that represents the root of a number c. nth root
4. A number b such that b 3 � a, where a is a number d. radicand
5. An exponent that is a rational number e. rational exponent
6. A number that is used to indicate which root of a f. radical
number is to be determined
Problem Set Complete each statement.
1. √___
49 � ___ because ___ 2 � 49. 2. √___
64 � ___ because ___ 2 � 64.
7, 7
3. √____
121 � ___ because ___ 2 � 121. 4. √____
196 � ___ because ___ 2 � 196.
5. 3 ��� 8 � ___ because ___ 3 � 8. 6.
3 ���� 64 � ___ because ___ 3 � 64.
7. 3 ������� �216 � ___ because ___ 3 � �216. 8. 3 ������ �27 � ___ because ___ 3 � �27.
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Calculate each root.
9. √___
25 10. √___
81
5
11. √____
144 12. √____
225
13. 3 ����� 125 14.
3 ����� 512
15. 3 ����� �1 16.
3 ������ �64
17. 4 ��� 1 18.
4 ���� 16
19. 5 ���� 32 20.
5 ������� �243
Rewrite each radical using a rational exponent.
21. √___
10 22. 3 ��� 6
10 1 __ 2
23. 6 ���� 25 24. √
___
50
25. 4 ��� 5 26. 8 ����� 200
27. 5 ���� 88 28.
10 ����� 36
29. 7 ��� x 30. √__
y
31. 9 ��� c 32. 3 ��� n
Chapter 9 ● Skills Practice 635
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Rewrite each power in radical form.
33. 9 1 __ 3 34. 5
1 __ 2
3 ��� 9
35. 20 1 __ 5 36. 41
1 __ 8
37. 8 1 __ 4 38. 100
1 ___ 10
39. 33 1 __ 2 40. 80
1 __ 7
41. a 1 __
6 42. b
1 __ 9
43. k 1 ___ 10
44. z
1 __ 5
Rewrite each power in radical form. Simplify your answer, if possible.
45. 16 3 __ 2 46. 5
7 __ 4
16 3 __ 2 � 16 (
1 __ 2 ) 3 � ( 1 6
1 __ 2 ) 3 � ( √
___ 16 ) 3 � 4 3 � 64
47. 12 2 __ 5
48. 8
4 __ 3
49. 2 5 __ 6
50. 15
6
__ 7
51. 9 5
__ 2
52. 27
2 __ 3
53. x 2 __ 9
54. q
3 __ 4
55. n 7 __ 2
56. y
8 __ 3
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Rewrite each expression using a rational exponent. Simplify your answer, if possible.
57. ( √__
8 ) 3 58. ( 3 ��� 9 ) 6
( √__
8 ) 3 � ( 8 1 __ 2 ) 3 � 8 (
1 __ 2 ) 3 � 8
3 __ 2
59. ( 5 ���� 10 ) 4 60. ( √
___
15 ) 5
61. ( 4 ����� 20 ) 3 62. ( 5 ��� 6 )
10
63. ( 6 ��� d ) 7 64. ( 8 ���� m ) 3
65. ( √__
w ) 6 66. ( 4 ��� t ) 4
67. ( 9 ��� h ) 3 68. ( 4 ��� g ) 6