Simplify each expression. Write all answers with positive exponents. Assume that all variables
represent positive real numbers. See Example 5.64. 65. 66.
67. 68. 69.
70. 71. 72.
73. 74. 75.
76. 77. 78.
79. 80. 81.
82. 83. 84.
85. 86. 87.
88. 89. 90.
Write with rational exponents, and then apply the properties of exponents. Assume that all
radicands represent positive real numbers. Give answers in exponential form. See Example 6.91. 92. 93. 94.
95. 96. 97. 98.
99. 100. 101. 102.
103.Show that, in general, by replacing awith 3 and bwith 4.
104.Suppose someone claims that must equal , since, when and
a true statement results:Explain why this is faulty reasoning.Solve each problem.
105.Meteorologists can determine the duration of a storm by using the function defined bywhere Dis the diameter of the storm in miles and Tis the time in hours. Find the duration
of a storm with a diameter of 16 mi. Round your answer to the nearest tenth of an hour.
106.The threshold weight T, in pounds, for a person is the weight above which the risk of
death increases greatly. The threshold weight in pounds for men aged 40 – 49 is related to
height hin inches by the function defined byWhat height corresponds to a threshold weight of 200 lb for a 46-yr-old man? Round
your answer to the nearest inch and then to the nearest tenth of a foot.h 1 T 2 = 1 1860.867T 2 1/3.T 1 D 2 =0.07D3/2,
2
n
an+bn= 2
n
1 n+ 0 n= 2
n
1 n= 1 = 1 + 0 =a+b.2 a+b a= 1 b=0,
n
an+bn2 a^2 +b^2 Za+b432 x 6432 x 433 24 x 43 35 2 yy# 23 yz 23 xz#z 3423 m 332 k
23 k^5
23 k^72 x^5
2 x^825 x^3 # 24 x 26 y^5 # 23 y^2
4 m5/3 1 m-2/3- 4 m-5/3 2 - 5 x7/6 1 x5/6-x-1/6 2 - 8 y11/7 1 y3/7-y-4/7 2k1/4 1 k3/2-k1/2 2 r3/5 1 r1/2+r3/4 2 6 a7/4 1 a-7/4+ 3 a-3/4 2a p2/3 1 p1/3+ 2 p4/3 2 z5/8 13 z5/8+ 5 z11/8 22 -^2 w-3/4x-5/8
w3/4x-1/2b- 3
ap-1/4q-3/2
3 -^1 p-^2 q-2/3b- 2
a
m-2/3
a-3/4b4
a 1 m-3/8a1/4 2 -^2b-3/2
c-5/3b2
1 b-1/4c-1/3 2 -^1z1/3z-2/3z1/6
1 z-1/6 23p1/5p7/10p1/2
1 p^32 - 1/51 a^2 b^52 - 1/4
1 a-^3 b^22 1/6m3/4n-1/4
1 m^2 n 2 1/21 p^32 1/4
1 p5/4 221 x2/3 22
1 x^22 7/31 r1/5s2/3 215
r^21 x1/4y2/5 220
x^2z3/4
z5/4#z-^2k1/3
k2/3#k-^1x2/3#x-1/4 x2/5#x-1/3
y7/3#y-4/3 r-8/9#r17/9
125 7/3
125 5/3
64 5/3
64 4/3
3 1/2# 3 3/2 6 4/3# 6 2/3