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Mathematics LibreTexts

0.04e: Exercises - Rational Exponents

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A: Radical to Exponential Notation

Exercise 0.4.1 

Express using rational exponents.

  1. 10
  2. 6
  1. 33
  2. 45
  1. 352
  2. 423
  1. 349
  2. 39
  1. 5x
  2. 6x
  1. 6x7
  2. 5x4
  1. 1x
  2. 13x2
Answers to odd exercises:
1. 101/2 3. 31/3 5. 52/3 7. 72/3 9. x1/5 11. x7/6 13. x1/2

B: Exponential to Radical Notation.

Exercise 0.4.2 

 Express in radical form.

  1. 101/2
  2. 111/3
  1. 72/3
  2. 23/5
  1. x3/4
  2. x5/6
  1. x1/2
  2. x3/4
  1. (1x)1/3
  2. (1x)3/5
  1. (2x+1)2/3
  2. (5x1)1/2
Answers to odd exercises:
15. 10 17. 349 19. 4x3 21. 1x 23. 3x 25. 3(2x+1)2

C: Exponential to Radical Form; then Simplify.

Exercise 0.4.3 

 Write as a radical and then simplify.

  1. 641/2
  2. 491/2
  3. (14)1/2
  4. (49)1/2
  1. 41/2
  2. 91/2
  3. (14)1/2
  4. (116)1/2
  1. 81/3
  2. 1251/3
  3. (127)1/3
  4. (8125)1/3
  5. (27)1/3
  1. (64)1/3
  2. 161/4
  3. 6251/4
  4. 811/4
  5. 161/4
  1. 100,0001/5
  2. (32)1/5
  3. (132)1/5
  4. (1243)1/5
Answers to odd exercises:
27. 8
29. 12
31. 12
33. 2
35. 2
37. 13
39. 3
41. 2
43. 13
45. 10
47. 12

 Write as a radical and then simplify.

  1. 93/2
  2. 43/2
  1. 85/3
  2. 272/3
  1. 163/2
  2. 322/5
  1. (116)3/4
  2. (181)3/4
  1. (27)2/3
  2. (27)4/3
  1. (32)3/5
  2. (32)4/5
Answers to odd exercises:
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.

  1. 53/251/2
  2. 32/337/3
  3. 51/251/3
  4. 21/623/4
  1. y1/4y2/5
  2. x1/2x1/4
  3. (u12v18)16
  4. ​​​​​​ (r9s12)13
  1. (81/2)2/3
  2. (36)2/3
  3. (x2/3)1/2
  4. (y3/4)4/5
  1. (y8)1/2
  2. (y6)2/3
  3. (4x2y4)1/2
  4. (9x6y2)1/2
  1. (2x1/3y2/3)3
  2. (8x3/2y1/2)2
  3. (36x4y2)1/2
  4. (8x3y6z3)1/3
Answers to odd exercises:
61. 25
63. 55/6
65. y13/20
67.u2v3
69. 2
71. x1/3
73. 1y4
75. 2xy2
77. 8xy2
79. 16x2y

 Perform the operations and simplify. Leave answers in exponential form.

  1. (27q32)43
  2. (64s37)16
  3. (a13b23)32
  1. (m43n12)34
  2. (16u13)34
  3. (625n83)34
  1. (4p13q12)32
  2. (9x25y35)52
  3. (16x2y1/3z2/3)3/2
  1. (81x8y4/3z4)3/4
  2. (100a2/3b4c3/2)1/2
  3. (125a9b3/4c1)1/3
Answers to odd exercises:
81. 81q2
83. a12b
85. 8u14
87. 8p12q34
85. 8u14
87. 8p12q34
89. 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.

  1. 511/352/3
  2. 29/221/2
  3. 2a2/3a1/6
  4. 3b1/2b1/3
  1. r52r12r32
  2. a34a14a104
  3. c53c13c23
  1. m74m54m24
  2. 113 y1/2y2/3y1/6
  3. x2/5x1/2x1/10
  1. xyx1/2y1/3
  2. x5/4yxy2/5
  3. 49a5/7b3/27a3/7b1/4
  4. 16a5/6b5/48a1/2b2/3
Answers to odd exercises:
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.

  1. (a3/4a1/2)4/3
  2. (b4/5b1/10)10/3 
  3. (4x2/3y4)1/2
  4. (27x3/4y9)1/3
  1. (27x3/4y9)1/3
  2. (36s15t32s95t12)12
  3. (27b23c52b73c12)13
  1. (8x53y1227x43y52)13
  2. (16m15n3281m95n12)14
  3. (9x2/3y6)3/2x1/2y
  1. (125x3y3/5)2/3xy1/3
  2. (27a1/4b3/2)2/3a1/6b1/2
  3. (25a2/3b4/3)3/2a1/6b1/3
Answers to odd exercises:
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.

  1. 3953
  2. 5525
  3. x3x
  1. y4y
  2. 3x24x
  3. 5x33x
  1. 310010
  2. 51634
  1. 3a2a
  2. 5b43b
  1. 3x25x3
  2. 4x33x2
  1. 516
  2. 39
  3. 352
Answers to odd exercises:
131. 15313
133. 6x5
135. 12x11
137. 610
139. 6a
141. 15x
143. 54
145. \(\sqrt [ 15 ] { 2 } )

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0.04e: Exercises - Rational Exponents is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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