Integer and Rational Number Exponents

Solution Set 3

1. `-256` 2. `256` 3. `1` 4. `-1`
5. `81/16` 6. `125/63` 7. `8` 8. `64`
9. `-3` 10. `-5` 11. `-16` 12. `-25`
13. `16` 14. `25` 15. `1/3` 16. `1/4`
17. `1/9` 18. `1/8` 19. `3/4` 20. `8/125`
21. `9/4` 22. `27/8`
23. `6x^7y^4` 24. `(8c^9)/(125)` 25. `(36x^4)/(y^4)`
26. `(2y^2)/(9x)` 27. `(y)/(3x)` 28. `(y^6)/(x^4)`
29. `1/a+1/b=>(a+b)/(ab)` 30. `b/(ac)` 31. `(16)/(b^2)`
32. `1` 33. `3|xy^3|` 34. `5a^2b`
35. `a^(1//2)b^(3//10)` 36. `(y^(2//3))/(x^(7//6))` 37. `a^2+7a`
38. `-8m^(2)-m` 39. `p-q` 40. `c^2-d^(2//3)`
41. `m^(2)n^(3//2)` 42. `(r^(1//2))/(s^(3))` 43. `1`
44. `r^(7n//2)` 45. `r^((m-n)//(mn))` 46. `s^(4//n)`
47. `2.1 xx 10^7` 48. `1.63 xx 10^8` 49. `9.5 xx 10^-4` 50. `8.21 xx 10^-8`
51. `6,500` 52. `0.00000000686` 53. `0.000217` 54. `3.75`
55. `sqrt(3x)` 56. `root3(6y)` 57. `5root4(xy)`
58. `2aroot5(bc)` 59. `root3((5w)^2)` 60. `root4((a+b)^3)`
61. `(17k)^(1//3)` 62. `4(3m)^(1//2)` 63. `a^(2//5)`
64. `3(5n)^(1//4)` 65. `((7a)/3)^(1//2)` 66. `((5b^2)/7)^(1//3)`
67. `3sqrt(5)` 68. `5sqrt(3)` 69. `2root3(3)` 70. `3root3(5)`
71. `-3root3(3)` 72. `-5root3(2)` 73. `-2root3(4)` 74. `-3root3(9)`
75. `2abs(xy)sqrt(6x)` 76. `3xy^2sqrt(2y)` 77. `-2ay^2root3(2y)` 78. `-3droot3(2c^2d^2)`
79. `-13sqrt(2)` 80. `46root3(4)` 81. `-10root4(3)` 82. `-5root3(5)`
83. `17yroot3(4y)` 84. `-5x^2root3(2x)` 85. `22x^2yroot3(y)` 86. `3a^2sqrt(ab)`
87. `29+11sqrt(5)` 88. `3+3sqrt(7)` 89. `2x-9` 90. `49-3a` 91. `50+10sqrt(6yz)+3z`
92. `45y-24sqrt(5y)+16` 93. `x+10sqrt(x-3)+22` 94. `x-6sqrt(x+7)+16` 95. `2x+14sqrt(2x+5)+54` 96. `9x+22sqrt(9x-2)+119`
97. `sqrt(2)` 98. `xsqrt(3)` 99. `sqrt(10)/6` 100. `sqrt(70)/20`
101. `(3root3(4))/(2)` 102. `root3(2)` 103. `(2root3(x))/x` 104. `root4(4y^3)/y`
105. `sqrt(5)/3` 106. `sqrt(35)/10` 107. `sqrt(6xy)/(9y)` 108. `sqrt(2cd)/(5d)`
109. `(3(sqrt(5)-sqrt(x)))/(5-x)` 110. `(5(sqrt(y)+sqrt(3)))/(y-3)` 111. `-(2sqrt(7)+7)/3` 112. `-30sqrt(6)+36`
113. Color Monitors
a. `2^16=65,536` b. `2^32=4,294,967,296`
114. Physiology
16,741,000
115. Astronomy
`1.97 xx 10^4`
116. Astronomy
`4.836 xx 10^8`
117. Finance
`$4,873.50`
118. Finance
a.`$5,368,709.12`
b.`$10,737,418.23`
119. Optics
a. `81%` b. `66%`
120. Food Science
a. `4.00` hours
b. Approximately `1.52` times longer.