C Challenge

You can define the rules for irrational exponents so that they have the same properties as rational exponents. Use those properties to simplify each expression.

91. ( 7 2 ) 2 open , 7 super square root of 2 end super , close super square root of 2 end super
92. 3 3 + 5 3 1 + 5 fraction 3 super 3 plus square root of 5 end super , over 3 super 1 plus square root of 5 end super end fraction
93. x 4 π x 2 π fraction x super 4 pi end super , over x super 2 pi end super end fraction
94. 5 2 3 ⋅ 25 − 3 5 super 2 square root of 3 end super , dot . 25 super negative square root of 3 end super
95. 9 1 2 9 super fraction 1 , over square root of 2 end fraction end super
96. ( 3 2 + 2 ) 2 − 2 open . 3 super 2 plus square root of 2 end super . close super 2 minus square root of 2 end super

97. Weather Using data for the effect of temperature and wind on an exposed face, the National Weather Service uses the following formula to determine wind chill.

    Wind Chill Index = 35.74 + 0.6215 T − 35.75 V 0.16 + 0.4275 T V 0.16 cap wind cap chill cap index . equals , 35.74 , plus , 0.6215 t minus . 35.75 v to the 0.16 . plus . 0.4275 t v to the 0.16

    T is the temperature in degrees Fahrenheit and V is the velocity of the wind in miles per hour. Frostbite occurs in about 15 minutes when the wind chill index is − 20 . negative 20 .  Find the wind velocity that produces a wind chill index of − 20 negative 20  when the temperature is 5 ° F . 5 degrees cap f .

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

98. What is the simplified value of ( 1 64 ) − 1 6 ? open , 1 sixty fourth , close super negative , 1 sixth end super . question mark
99. What positive value of b makes 9 x 2 − b x + 4 9 x squared , minus b x plus 4  a perfect square trinomial?
100. How many real roots does the cubic polynomial equation x 3 − 7 x 2 + 13 x − 4 = 0 x cubed , minus , 7 x squared , plus 13 x minus 4 equals 0  have?
101. What is the y-value of the y-intercept of the graph of f ( x ) = 4 | x − 2 | − 5 ? f open x close equals 4 vertical line x minus 2 vertical line negative 5 question mark

Mixed Review

See Lesson 6-3.

Simplify.

102. 6 3 3 − 2 3 3 6 , cube root of 3 , , minus 2 , cube root of 3 ,
103. 3 18 + 2 72 3 square root of 18 plus 2 square root of 72
104. ( 5 − 1 ) ( 5 + 4 ) open , square root of 5 minus 1 , close . open , square root of 5 plus 4 , close
105. ( 1 − 2 2 ) ( 1 + 2 2 ) open . 1 minus 2 square root of 2 . close . open . 1 plus 2 square root of 2 . close
106. 2 12 − 4 27 2 square root of 12 minus 4 square root of 27
107. 162 4 + 3 32 4 the fourth , root of 162 , , plus 3 , the fourth , root of 32 ,

See Lesson 4-4.

Factor each expression completely.

108. 4 x 3 − 8 x 2 + 16 x 4 x cubed , minus , 8 x squared , plus 16 x
109. x 2 + 4 x + 4 x squared , plus 4 x plus 4
110. x 2 − 18 x + 81 x squared , minus 18 x plus 81
111. 16 a 2 − 9 b 2 16 eh squared , minus , 9 b squared
112. 25 x 2 − 40 x y + 16 y 2 25 x squared , minus 40 x y plus , 16 y squared
113. 9 x 2 + 48 x + 64 9 x squared , plus 48 x plus 64

See Lesson 4-5.

Get Ready! To prepare for Lesson 6-5, do Exercises 114–119.

Solve by factoring. Check your answers.

114. x 2 = − x + 6 x squared , equals negative x plus 6
115. x 2 = 5 x + 14 x squared , equals 5 x plus 14
116. 2 x 2 + x = 3 2 x squared , plus x equals 3
117. 3 x 2 − 2 = 5 x 3 x squared , minus 2 equals 5 x
118. 4 x 2 = − 8 x + 5 4 x squared , equals negative 8 x plus 5
119. 6 x 2 = 5 x + 6 6 x squared , equals 5 x plus 6

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