87. 1. Use the property for dividing powers with the same base to write a 0 a n fraction eh to the , over eh to the n end fraction  as a power of a.
    2. Use the definition of a zero exponent to simplify a 0 a n . fraction eh to the , over eh to the n end fraction . .
    3. Reasoning Explain how your results from parts (a) and (b) justify the definition of a negative exponent.

C Challenge

88. Reasoning Use the division property to show why 0 0 0 to the  is undefined.

Simplify each expression.

89. n x + 2 ÷ n x n super x plus 2 end super . divides , n to the x
90. n 5   x ÷ n x n to the fifth , to the x , divides , n to the x
91. ( x n x n − 2 ) 3 open . fraction x to the n , over x super n minus 2 end super end fraction . close cubed
92. ( m 4 m 5 ) m 2 fraction open . fraction m to the fourth , over m to the fifth end fraction . close , over m squared end fraction
93. Astronomy The density of an object is the ratio of its mass to its volume. Neptune has a mass of 1.02 × 10 26 1.02 , times , 10 to the twenty sixth  kg. The radius of Neptune is 2.48 × 10 4 2.48 , times , 10 to the fourth  km. What is the density of Neptune in grams per cubic meter? (Hint: V = 4 3 π r 3 v equals , 4 thirds , pi , r cubed )

Standardized Test Prep

SAT/ACT

94. Which expression is equivalent to ( 2 x ) 5 x 3 ? fraction open , 2 x , close to the fifth , over x cubed end fraction . question mark

    1. 2 x 2 2 , x squared
    2. 32 x 2 32 , x squared
    3. 2 x 8 2 , x to the eighth
    4. 32 x − 2 32 , x super negative 2 end super

95. Which equation is an equation of the line that contains the point (8, – 3 en dash 3 ) and is perpendicular to the line y = – 4 x + 5 ? y equals en dash 4 x plus 5 question mark

    6. y = − 1 4 x − 1 y equals negative , 1 fourth , x minus 1
    7. y = 1 4 x + 35 4 y equals , 1 fourth , x plus , 35 over 4
    8. y = 1 4 x − 5 y equals , 1 fourth , x minus 5
    9. y = 4 x − 35 y equals 4 x minus 35

96. What is the solution of the system of equations y = – 3 x + 5 y equals en dash 3 x plus 5  and y = – 4 x – 1 ? y equals en dash 4 x en dash 1 question mark

    1. (23, 6)
    2. (6, 23)
    3. ( − 6 , 23 ) open negative 6 comma 23 close
    4. ( − 6 , − 23 ) open negative 6 comma negative 23 close
97. Short Response 97. You have 8 bags of grass seed. Each bag covers 1200 ft 2 1200 , ft squared  of ground. The function A ( b ) = 1200 b eh open b close equals , 1200 , b  represents the area A ( b ) , eh open b close comma  in square feet, that b bags cover. What domain and range are reasonable for the function? Explain.

Mixed Review

See Lesson 7-4.

Simplify each expression.

98. ( 2 m −   7 ) 3 open 2 , m to the minus , to the seventh , close cubed
99. 2 ( 3 s − 2 ) − 3 2 . open . 3 , s super negative 2 end super . close super negative 3 end super
100. ( 4 3 c 2 ) − 1 open . 4 cubed , c squared . close super negative 1 end super
101. ( − 3 ) 2 ( r 5 ) 2 open , negative 3 , close squared . open , r to the fifth , close squared
102. ( 7 0 n − 3 ) 2 ( n 7 ) 3 open . 7 to the . n super negative 3 end super . close squared . open , n to the seventh , close cubed

See Lesson 6-1.

Solve each system by graphing.

103. y = 3 x y = − 2 x table with 2 rows and 1 column , row1 column 1 , y equals 3 x , row2 column 1 , y equals negative 2 x , end table
104. y = 2 x + 1 y = x − 3 table with 2 rows and 1 column , row1 column 1 , y equals 2 x plus 1 , row2 column 1 , y equals x minus 3 , end table
105. y = 5 x = 3 table with 2 rows and 1 column , row1 column 1 , y equals 5 , row2 column 1 , x equals 3 , end table
106. y = 7 y = 8 table with 2 rows and 1 column , row1 column 1 , y equals 7 , row2 column 1 , y equals 8 , end table

Get Ready! To prepare for Lesson 7-6, do Exercises 107–110.

See Lesson 4-4.

Graph each function.

107. y = 4 x y equals 4 x
108. y = 5 x y equals 5 x
109. y = − 3 x y equals negative 3 x
110. y = 1.5 x y equals 1.5 x

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