0.4e: Exercises - Rational Exponents
- Page ID
- 38226
A: Radical to Exponential Notation
Exercise \(\PageIndex{1}\)
\( \bigstar \) Express using rational exponents.
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- Answers to odd exercises:
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1. \(10 ^ { 1 / 2 } \) 3. \(3 ^ { 1 / 3 } \) 5. \(5 ^ { 2 / 3 } \) 7. \(7 ^ { 2 / 3 } \) 9. \(x ^ { 1 / 5 } \) 11. \(x ^ { 7 / 6 } \) 13. \(x ^ { - 1 / 2 }\)
B: Exponential to Radical Notation.
Exercise \(\PageIndex{2}\)
\( \bigstar \) Express in radical form.
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- Answers to odd exercises:
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15. \(\sqrt { 10 }\) 17. \(\sqrt [ 3 ] { 49 } \) 19. \(\sqrt [ 4 ] { x ^ { 3 } }\) 21. \(\dfrac { 1 } { \sqrt { x } } \) 23. \(\sqrt [ 3 ] { x } \) 25. \(\sqrt [ 3 ] { ( 2 x + 1 ) ^ { 2 } } \)
C: Exponential to Radical Form; then Simplify.
Exercise \(\PageIndex{3}\)
\( \bigstar \) Write as a radical and then simplify.
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- Answers to odd exercises:
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27. \(8\)
29. \(\dfrac{1}{2} \)31. \(\dfrac{1}{2} \\[5pt]\)
33. \(2 \)35. \(2\)
37. \( \dfrac{1}{3} \)39. \(-3 \\[5pt]\)
41. \(2 \)43. \(\dfrac{1}{3} \\[5pt]\)
45. \( 10 \)47. \(\dfrac{1}{2} \)
\( \bigstar \) 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. \(\dfrac{1}{8} \) 57. \(9 \) 59. \(-8\)
D: Exponential Operations. PRODUCTS and POWERS of Products
Exercise \(\PageIndex{4}\)
\( \bigstar \) Perform the operations and simplify. Leave answers in exponential form.
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- Answers to odd exercises:
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61. \(25 \\[5pt]\)
63. \(5 ^ { 5 / 6 } \)65. \(y ^ { 13 / 20 } \\[5pt]\)
67.\(u^{2}v^{3} \)69. \(2 \\[5pt]\)
71. \(x ^ { 1 / 3 } \)73. \(\dfrac { 1 } { y ^ { 4 } } \\[5pt]\)
75. \(2 x y ^ { 2 }\)77. \(8 x y ^ { 2 } \\[5pt]\)
79. \(\dfrac { 1 } { 6 x ^ { 2 } y } \)
\( \bigstar \) Perform the operations and simplify. Leave answers in exponential form.
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- Answers to odd exercises:
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81. \(81 q^{2} \\[2pt]\)
83. \(a^{\tfrac{1}{2}} b\)85. \(8 u^{\tfrac{1}{4}} \\[5pt]\)
87. \(8 p^{\tfrac{1}{2}} q^{\tfrac{3}{4}} \)85. \(8 u^{\tfrac{1}{4}} \\[5pt]\)
87. \(8 p^{\tfrac{1}{2}} q^{\tfrac{3}{4}}\)89. \(\dfrac { y ^ { 1 / 2 } } { 64 x ^ { 3 } z } \\[5pt]\)
91. \(\dfrac { a ^ { 1 / 3 } b ^ { 3 / 4 } } { 10 b ^ { 2 } }\)
E: Exponential Operations. QUOTIENTS and POWERS of Quotients
Exercise \(\PageIndex{5}\)
\( \bigstar \) 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. \(2 a ^ { 1 / 2 } \) 105. \(r^{\frac{7}{2}}\) 107. \(c^{2} \) 109. \(y\) 111. \(x ^ { 1 / 2 } y ^ { 2 / 3 } \) 113. \(7 a ^ { 2/7 } b ^ { 5 / 4 } \)
\( \bigstar \) Perform the operations and simplify. Leave answers in exponential form.
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- Answers to odd exercises:
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115. \(a ^ { 1 / 3 } \) 117. \(\dfrac { 2 x ^ { 1 / 3 } } { y ^ { 2 } } \) 119. \(\dfrac{6 s}{t} \) 121. \(\dfrac{2x}{3y} \) 123. \(27 x ^ { 1 / 2 } y ^ { 8 } \) 125. \(9 b ^ { 1 / 2 } \)
F: Radical to Exponential Form Operations.
Exercise \(\PageIndex{6} \)
\( \bigstar \) Rewrite in exponential form and then perform the operations.
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- Answers to odd exercises:
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131. \(\sqrt [ 15 ] { 3 ^ { 13 } } \\[5pt]\)
133. \(\sqrt [ 6 ] { x ^ { 5 } } \)135. \(\sqrt [ 12 ] { x ^ { 11 } } \\[5pt]\)
137. \(\sqrt [ 6 ] { 10 }\)139. \(\sqrt [ 6 ] { a } \\[5pt]\)
141. \(\sqrt [ 15 ] { x }\)143. \(\sqrt [ 5 ] { 4 } \\[5pt]\)
145. \(\sqrt [ 15 ] { 2 } )
.\( \bigstar \)