0.04e: Exercises - Rational Exponents
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A: Radical to Exponential Notation
Exercise 0.4.1
★ Express using rational exponents.
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- Answers to odd exercises:
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1. 101/2 3. 31/3 5. 52/3 7. 72/3 9. x1/5 11. x7/6 13. x−1/2
B: Exponential to Radical Notation.
Exercise 0.4.2
★ Express in radical form.
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- Answers to odd exercises:
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15. √10 17. 3√49 19. 4√x3 21. 1√x 23. 3√x 25. 3√(2x+1)2
C: Exponential to Radical Form; then Simplify.
Exercise 0.4.3
★ Write as a radical and then simplify.
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- Answers to odd exercises:
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27. 8
29. 1231. 12
33. 235. 2
37. 1339. −3
41. 243. 13
45. 1047. 12
★ Write as a radical and then simplify.
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- Answers to odd exercises:
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49. 27 51. 32 53. 64 55. 18 57. 9 59. −8
D: Exponential Operations. PRODUCTS and POWERS of Products
Exercise 0.4.4
★ Perform the operations and simplify. Leave answers in exponential form.
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- Answers to odd exercises:
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61. 25
63. 55/665. y13/20
67.u2v369. 2
71. x1/373. 1y4
75. 2xy277. 8xy2
79. 16x2y
★ Perform the operations and simplify. Leave answers in exponential form.
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- Answers to odd exercises:
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81. 81q2
83. a12b85. 8u14
87. 8p12q3485. 8u14
87. 8p12q3489. y1/264x3z
91. a1/3b3/410b2
E: Exponential Operations. QUOTIENTS and POWERS of Quotients
Exercise 0.4.5
★ Perform the operations and simplify. Leave answers in exponential form.
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- Answers to odd exercises:
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101. 125 103. 2a1/2 105. r72 107. c2 109. y 111. x1/2y2/3 113. 7a2/7b5/4
★ Perform the operations and simplify. Leave answers in exponential form.
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- Answers to odd exercises:
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115. a1/3 117. 2x1/3y2 119. 6st 121. 2x3y 123. 27x1/2y8 125. 9b1/2
F: Radical to Exponential Form Operations.
Exercise 0.4.6
★ Rewrite in exponential form and then perform the operations.
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- Answers to odd exercises:
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131. 15√313
133. 6√x5135. 12√x11
137. 6√10139. 6√a
141. 15√x143. 5√4
145. \(\sqrt [ 15 ] { 2 } )
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