50 CHAPTER R Review of Basic Concepts Simplify each expression. Write answers without negative exponents. Assume all variables represent positive real numbers. See Examples 8 and 9. 83. 82/3 84. 274/3 85. 1003/2 86. 643/2 87. -813/4 88. 1-322-4/5 89. a 27 64b -4/3 90. a 121 100b -3/2 91. 31/2 # 33/2 92. 64/3 # 62/3 93. 645/3 644/3 94. 1257/3 1255/3 95. y7/3 # y-4/3 96. r-8/9 # r17/9 97. k1/3 k2/3 # k-1 98. z3/4 z5/4 # z-2 99. 1x1/4y2/5220 x2 100. 1r1/5s2/3215 r2 101. 1x2/322 1x227/3 102. 1p321/4 1p5/422 103. a 16m3 n b 1/4a9n-1 m2 b 1/2 104. a 254a3 b2 b 1/8a42b-5 a2 b 1/4 105. p1/5p7/10p1/2 1p32-1/5 106. z1/3z-2/3z1/6 1z-1/623 (Modeling) Solve each problem. 107. Holding Time of Athletes A group of ten athletes were tested for isometric endurance by measuring the length of time they could resist a load pulling on their legs while seated. The approximate amount of time (called the holding time) that they could resist the load was given by the formula t = 31,293w-1.5, where w is the weight of the load in pounds and the holding time t is measured in seconds. (Data from Townend, M. Stewart, Mathematics in Sport, Chichester, Ellis Horwood Limited.) (a) Determine the holding time, to the nearest second, for a load of 25 lb. (b) When the weight is doubled, by what factor is the holding time changed? 108. Duration of a Storm Suppose that meteorologists approximate the duration of a particular storm using the formula T = 0.07D3/2, where T is the time (in hours) that a storm of diameter D (in miles) lasts. (a) How many minutes is a storm 4 mi in diameter expected to last? (b) A thunderstorm is predicted for a farming community. The crops need at least 1.5 hr of rain. Local radar shows that the storm is 7 mi in diameter. Will it rain long enough to meet the farmers’ need? Concept Check Calculate each value mentally. 109. 10.2532140032 110. 1242210.522 111. 4.25 2.15 112. 154 54 113. 0.22/3 # 402/3 114. 0.13/2 # 903/2 115. 22/3 20002/3 116. 203/2 53/2
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