A12 APPENDIX Review In Problems 81–84, use the formula C F 5 9 32 ( ) = − for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of each Fahrenheit temperature. 81. F 32 = ° 82. F 212 = ° 83. F 77 = ° 84. F 4 = − ° In Problems 85–96, simplify each expression. 85. 4 2 ( ) − 86. 42 − 87. 4 2− 88. 4 2 − − 89. 3 3 6 4 ⋅ − 90. 4 4 2 3 ⋅ − 91. 3 2 1 ( ) − − 92. 2 1 3 ( ) − − 93. 25 94. 36 95. 4 2 ( ) − 96. 3 2 ( ) − In Problems 107–118, find the value of each expression if x 2 = and y 1. = − 107. xy 2 1− 108. x y 3 1 − − 109. x y 2 2 + 110. x y2 2 111. xy 2 ( ) 112. x y 2 ( ) + 113. x2 114. x 2 ( ) 115. x y 2 2 + 116. x y 2 2 + 117. xy 118. yx 119. Find the value of the expression x x x 2 3 5 4 3 2 − + − if x 2. = What is the value if x 1? = 120. Find the value of the expression x x x 4 3 2 3 2 + − + if x 1. = What is the value if x 2? = 121. What is the value of 666 222 ? 4 4 ( ) ( ) 122. What is the value of 0.1 20 ? 3 3 ( ) ( ) In Problems 123–130, use a calculator to evaluate each expression. Round your answer to three decimal places. 123. 8.2 6 ( ) 124. 3.7 5 ( ) 125. 6.1 3 ( )− 126. 2.2 5 ( )− 127. 2.8 6 ( ) − 128. 2.8 6 ( ) − 129. 8.11 4 ( ) − − 130. 8.11 4 ( ) − − 131. Area of a Rectangle The area A of a rectangle is the product of its length l and its width w. l w A 132. Perimeter of a Rectangle The perimeter P of a rectangle is twice the sum of its length l and its width w. 133. Circumference of a Circle The circumference C of a circle is the product of π and its diameter d. C d 134. Area of a Triangle The area A of a triangle is one-half the product of its base b and its height h. h b 135. Area of an Equilateral Triangle The area A of an equilateral triangle is 3 4 times the square of the length x of one side. x x x In Problems 131–140, express each statement as an equation involving the indicated variables. Applications and Extensions In Problems 97–106, simplify each expression. Express the answer so that all exponents are positive.Whenever an exponent is 0 or negative, assume that the base is not 0. 97. x8 3 2 ( ) 98. x4 2 1 ( ) − − 99. x y2 1 2 ( ) − 100. x y1 3 ( ) − 101. x y xy 2 3 4 102. x y xy 2 2 − 103. x yz xy z 2 3 3 4 2 2 3 ( ) ( ) − 104. x yz x y 4 2 2 1 3 4 ( ) − − 105. x y 3 4 1 1 2 − − − 106. x y 5 6 2 2 3 − − −
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