0.02e: Exercises - Whole number exponents
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A: Zero and Negative Exponents
Exercise 0.2.1
★ Simplify. (Assume all variables represent nonzero numbers.)
1. −5x0 2. 3x2y0 |
3. −2x−3 4. (−2x)−2 |
5. 10x−3y2 6. −3x−5y−2 |
7. 3x−2y2z−1 8. −5x−4y−2z2 |
- Answers to odd exercises.
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1. −5 3. −2x3 5. 10y2x3 7. 3y2x2z
B: Product Rule
Exercise 0.2.2
★ Simplify. (Assume all variables represent nonzero numbers.)
11. 104⋅107 12. 73⋅72 13. x3⋅x2 14. y5⋅y3 |
15. a4⋅a−5⋅a2 16. b−8⋅b3⋅b4 17. 5x2y⋅3xy2 18. −10x3y2⋅2xy |
19. −6x2yz3⋅3xyz4 20. 2xyz2(−4x2y2z) 21. 3xny2n⋅5x2y 22. 8x5nyn⋅2x2ny |
23. (2x+3)4(2x+3)9 24. (3y−1)7(3y−1)2 25. (a+b)3(a+b)5 26. (x−2y)7(x−2y)3 |
- Answers to odd exercises.
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11. 1011
13. x5
15. a
17. 15x3y3
19. −18x3y2z7
21. 15xn+2y2n+1
23. (2x+3)13
25. (a+b)8
C: Quotient Rule
Exercise 0.2.3
★ Simplify. (Assume all variables represent nonzero numbers.)
31. 102⋅104105 32. 75⋅7972 33. a8⋅a6a5 34. b4⋅b10b8 |
35. a8⋅a−3a−6 36. b−10⋅b4b−2 37. 25x−3y25x−1y−3 38. −9x−1y3z−53x−2y2z−1 |
39. 40x5y3z4x2y2z 40. 8x2y5z316x2yz 41. 24a8b3(a−5b)108a5b3(a−5b)2 42. 175m9n5(m+n)725m8n(m+n)3 |
43. x2n⋅x3nxn 44. xn⋅x8nx3n |
- Answers to odd exercises.
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31. 10
33. a9
35. a11
37. 5y5x2
39. 10x3y
41. 3a3(a−5b)8
43. x4n
D: Power Rule for Products
Exercise 0.2.4
★ Simplify. (Assume all variables represent nonzero numbers.)
51. (x5)3 52. (y4)3 53. (x4y5)3 54. (x7y)5 55. (−5x)0 56. (3x2y)0 |
57. (x2y3z4)4 58. (xy2z3)2 59. (−5x2yz3)2 60. (−2xy3z4)5 61. (x⋅x3⋅x2)3 62. (y2⋅y5⋅y)2 |
63. (−2x4y2z)6 64. (−3xy4z7)5 65. (−2a2b0c3)5 66. (−3a4b2c0)4 67. (−5x−3y2z)−3 68. (−7x2y−5z−2)−2 69. (x2yz5)n |
70. (xy2z3)2n 71. a2⋅(a4)2a3 72. a⋅a3⋅a2(a2)3 73. (9x3y2z0)23xy2 74. (−5x0y5z)325y2z0 |
- Answers to odd exercises.
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51. x15
53. x12y15
55. 1
57. x8y12z16
59. 25x4y2z6
61. x18
63. 64x24y12z6
65. −32a10c15
67. −x9125y6z3
69. x2nynz5n
71. a7
73. 27x5y2
E: Power Rule for Quotients of Products
Exercise 0.2.5
★ Simplify. (Assume all variables represent nonzero numbers.)
81. (−3ab22c3)3 82. (−10a3b3c2)2 83. (−2xy4z3)4 84. (−7x9yz4)3 |
85. (12x3y2z2x7yz8)3 86. (150xy8z290x7y2z)2 87. (2x−3zy2)−5 88. (5x5z−22y−3)−3 |
89. (xy2z3)n 90. (2x2y3z)n 91. (−9a−3b4c−23a3b5c−7)−4 92. (−15a7b5c−83a−6b2c3)−3 |
- Answers to odd exercises:
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81. −27a3b68c9
83. 16x4y16z12
85. 216y3x12z21
87. x15y1032z5
89. xny2nz3n
91. a24b481c20