In exercises 1 to 22, evaluate each expression.
1. `-4^4`	2. `(-4)^4`	3. `((2^2*3^(-5))/(2^(-3)*5^4))^0`	4. `-7^0`
5. `(4/9)^-2`	6. `((5^(-3)*7)/3^(-2))^(-1)`	7. `4^(3//2)`	8. `16^(3//2)`
9. `-9^(1//2)`	10. `-25^(1//2)`	11. `-64^(2//3)`	12. `-125^(2//3)`
13. `(-64)^(2//3)`	14. `(-125)^(2//3)`	15. `9^(-1//2)`	16. `16^(-1//2)`
17. `27^(-2//3)`	18. `4^(-3//2)`	19. `(9/16)^(1//2)`	20. `(4/25)^(3//2)`
21. `(8/27)^(-2//3)`		22. `(4/9)^(-3//2)`

In exercises 23 to 46, simplify each exponential expression.
23. `(2x^2y^3)(3x^5y)`	24. `((2ab^2c^3)/(5ab^2))^3`	25. `(3xy^(-3))^2/(2xy)^(-2)`
26. `(2x^(-3)y^0)(3^(-1)xy)^2`	27. `((3x)/y)^(-1)`	28. `(x^2y^(-3))^(-2)`
29. `a^(-1)+b^(-1)`	30. `(4a^2(bc)^(-1))/((-2)^2a^3b^(-2)c)`	31. `(2ab^(-3))^2(-2a^(-1)b^2)^2`
32. `[(b^(-3)/a^2)^2(a^(-2)/ab)^(-1)]^0`	33. `(81x^4y^12)^(1//4)`	34. `(625a^8b^4)^(1//4)`
35. `(a^(3//4)b^(1//2))/(a^(1//4)b^(1//5))`	36. `(x^(1//3)y^(5//6))/(x^(3//2)y^(1//6))`	37. `a^(1//3)(a^(5//3)+7a^(2//3))`
38. `m^(3//4)(m^(1//4)-8m^(5//4))`	39. `(p^(1//2)+q^(1//2))(p^(1//2)-q^(1//2))`	40. `(c+d^(1//3))(c-d^(1//3))`
41. `((m^2n^4)/(m^(-2)n))^(1//2)`	42. `((r^2s^(-2))/(rs^4))^(1//2)`	43. `(x^(n+1//2)*x^(-n))/(x^(1//2))`
44. `(r^(n//2)*r^(2n))/(r^(-n))`	45. `(r^(1//n))/(r^(1//m))`	46. `(s^(2//n))/(s^(-2//n))`

In exercises 47 to 50, write each number in scientific notation.
47. `21,000,000`	48. `163,000,000`	49. `0.00095`	50. `0.0000000821`

In exercises 51 to 54, change each number from scientific notation to decimal notation.
51. `6.5 xx 10^3`	52. `6.86 xx 10^(-9)`	53. `2.17 xx 10^(-4)`	54. `3.75 xx 10^0`

In exercises 55 to 60, write each exponential expression in radical form.
55. `(3x)^(1//2)`	56. `(6y)^(1//3)`	57. `5(xy)^(1//4)`
58. `2a(bc)^(1//5)`	59. `(5w)^(2//3)`	60. `(a+b)^(3//4)`

In exercises 61 to 66, write each radical in exponential form.
61. `root3(17k)`	62. `4sqrt(3m)`	63. `root5(a^2)`
64. `3root4(5n)`	65. `sqrt((7a)/3)`	66. `root3((5b^2)/7)`

In exercises 67 to 78, simplify each radical.
67. `sqrt(45)`	68. `sqrt(75)`	69. `root3(24)`	70. `root3(135)`
71. `root3(-81)`	72. `root3(-250)`	73. `-root3(32)`	74. `-root3(243)`
75. `sqrt(24x^3y^2)`	76. `sqrt(18x^2y^5)`	77. `-root3(16a^3y^7)`	78. `-root3(54c^2d^5)`

In exercises 79 to 86, simplify each radical and then combine like radicals.
79. `2sqrt(32)-3sqrt(98)`	80. `5root3(32)+2root3(108)`
81. `-8root4(48)+2root4(243)`	82. `2root3(40)-3root3(135)`
83. `4root3(32y^4)+3yroot3(108y)`	84. `-3xroot3(54x^4)+2root3(16x^7)`
85. `3xroot3(8x^3y^4)+4yroot3(64x^6y)`	86. `4sqrt(a^5b)-a^2sqrt(ab)`

In exercises 87 to 96, find the indicated product of the radical expressions. Express each result in simplest form.
87. `(sqrt(5)+8)(sqrt(5)+3)`	88. `(sqrt(7)+4)(sqrt(7)-1)`
89. `(sqrt(2x)+3)(sqrt(2x)-3)`	90. `(7-sqrt(3a))(7+sqrt(3a))`
91. `(5sqrt(2y)+sqrt(3z))^2`	92. `(3sqrt(5y)-4)^2`
93. `(sqrt(x-3)+5)^2`	94. `(sqrt(x+7)-3)^2`
95. `(sqrt(2x+5)+7)^2`	96. `(sqrt(9x-2)+11)^2`

In exercises 97 to 112, simplify each expression by rationalizing the denominator. Write the result in simplest form.
97. `(2)/(sqrt(2))`	98. `(3x)/(sqrt(3))`	99. `sqrt(5/18)`	100. `sqrt(7/40)`
101. `(3)/(root3(2))`	102. `(2)/(root3(4))`	103. `(4)/(root3(8x^2))`	104. `(2)/(root4(4y))`
105. `sqrt(10/18)`	106. `sqrt(14/40)`	107. `sqrt((2x)/(27y))`	108. `sqrt((4c)/(50d))`
109. `(3)/(sqrt(5)+sqrt(x))`	110. `(5)/(sqrt(y)-sqrt(3))`	111. `(sqrt(7))/(2-sqrt(7))`	112. `(6sqrt(6))/(5+sqrt(6))`

113. Color Monitors The number of colors that a computer with a color monitor can display is sometimes indicated in bits (a bit is a binary digit). For example, a computer with an 8-bit color interface can display `2^8=256` colors. Determine how many colors each of the following can display.
a. A computer with a 16-bit interface.	b. A computer with a 32-bit interface.

114. Physiology It has been estimated that the human eye can detect 36,000 different colors. How many colors (to the nearest 1000) would go undetected by a human using a computer with a 24-bit color interface? (See excercise 113.)

115. Astronomy Pluto is `5.91 xx 10^12` meters from the Sun. The speed of light is `3.00 xx 10^8` meters per second. Find the time it takes light from the Sun to reach Pluto.

116. Astronomy The Earth's mean distance from the Sun is `9.3 xx 10^7` miles. The distance is called the astronomical unit (AU). Jupiter is 5.2 AU from the Sun. Find the distance in miles from the Sun to Jupiter.

117. Finance A principal `P` invested at an annual interest rate `r` compounded `n` times per year yields a balance `A` given by the formula `A=P(1+r/n)^(n)` Find the balance after 1 year when `$4500` is deposited in an account with an annual interest rate of `8%` that is compounded monthly.

118. Finance You plan to save `1¢` the first day of a month, `2¢` the second day, and `4¢` the third day and to continue this pattern of saving twice what you saved on the previous day for every day in a month that has 30 days.

a. How much money will you need to save on the 30th day?

b. How much money would you have after 30 days?

(Hint: Note that after 2 days you will have saved `2^2-1=3¢` and that after 3 days you will have saved `2^3-1=7¢`.)

119. Optics The percent `P` of light that will pass through a frosted glass is given by the equation `P=10^(-kd)`, where `d` is the thickness of the glass in centimeters and `k` is a constant that depends on the glass. Find, to the nearest percent, the amount of light that will pass through the frosted glass for which
a. `k=0.15`, `d=0.6` centimeters.	b. `k=0.15`, `d=1.2` centimeters.

120. Food Science The number of hours `h` needed to cook a pot roast that weighs `p` pounds can be approximated by using the formula `h=0.9p^(0.6)`.

a. Find the time (to the nearest hundredth of an hour) required to cook a 12-pound pot roast.

b. If pot roast `A` weighs twice as much as pot roast `B`, then roast `A` should be cooked for a period of time that is how many times longer than time required for roast `B` to cook?