C Challenge

Simplify each expression.

65. 3 x · 3 2 − x · 3 2 3 to the x , middle dot . 3 super 2 minus x end super . middle dot , 3 squared
66. 2 n · 2 n + 2 · 2 2 to the n , middle dot . 2 super n plus 2 end super . middle dot 2
67. 3 x · 2 y · 3 2 · 2 x 3 to the x , middle dot , 2 to the y , middle dot , 3 squared , middle dot , 2 to the x
68. ( a + b ) 2 ( a + b ) − 3 open eh plus b close squared . open eh plus b close super negative 3 end super
69. ( t + 3 ) 7 ( t + 3 ) − 5 open t plus 3 close to the seventh . open t plus 3 close super negative 5 end super
70. 5 x + 1 · 5 1 − x 5 super x plus 1 end super . middle dot . 5 super 1 minus x end super
71. Nature A book shows an enlarged photo of a carpenter bee. A carpenter bee is about 6 × 10 − 3 6 times , 10 super negative 3 end super  m long. The photo is 13.5 cm long. About how many times as long as a carpenter bee is the photo?

Standardized Test Prep

SAT/ACT

72. What is the simplified form of ( 2 x 2 y 3 2 , x squared , y cubed )( 4 x y − 2 4 x y super negative 2 end super )?

    1. 6 x 3 y 5 6 , x cubed , y to the fifth
    2. 6 x 2 y 6 6 , x squared , y to the sixth
    3. 8 x 2 y 8 , x squared , y
    4. 8 x 3 y 8 , x cubed , y

73. What is the x-intercept of the graph of 5 x − 3 y = 30 ? 5 x minus 3 y equals 30 question mark

    6. − 10 negative 10
    7. − 6 negative 6
    8. 6
    9. 10

74. At the Athens Olympics, the winning time for the women's 100-m hurdles was 2.06 × 10 − 1 2.06 , times , 10 super negative 1 end super  min. Which number is another way to express this time in minutes?

    1. 0.206
    2. 20.6
    3. 206 × 10 1 206 times , 10 to the first
    4. 206 × 10 − 2 206 times , 10 super negative 2 end super

75. What is the solution of 4 x − 5 = 2 x + 13 ? 4 x minus 5 equals 2 x plus 13 question mark

    6. 3
    7. 4
    8. 9
    9. 32

Extended Response

76. Bill's company packages its circular mirrors in boxes with square bottoms, as shown below. Show your work for each answer.

    1. What is an expression for the area of the bottom of the box?
    2. If the mirror has a radius of 4 in., what is the area of the bottom of the box?
    3. The area of the bottom of a second box is 196 in . 2 . in . squared , .  What is the diameter of the largest mirror the box can hold?

Mixed Review

See Lesson 7-2.

Write each number in scientific notation.

77. 2,358,000
78. 0.00465
79. 0.00007
80. 5.1 billion

See Lesson 4-7.

Find the third, seventh, and tenth terms of the sequence described by each rule.

81. A ( n ) = 10 + ( n − 1 ) ( 4 ) eh open n close equals 10 plus open n minus 1 close open 4 close
82. A ( n ) = − 5 + ( n − 1 ) ( 2 ) eh open n close equals negative 5 plus open n minus 1 close open 2 close
83. A ( n ) = 1.2 + ( n − 1 ) ( − 4 ) eh open n close equals 1.2 plus open n minus 1 close open negative 4 close

Get Ready! To prepare for Lesson 7-4, do Exercises 84–87.

See Lesson 7-1.

Simplify each expression.

84. ( − 2 ) − 4 open negative 2 close super negative 4 end super
85. 5 x y 0 5 x , y to the
86. 4 m − 1 n 2 4 , m super negative 1 end super . n squared
87. − 3 x 3 y − 2 z 6 negative 3 , x cubed . y super negative 2 end super . z to the sixth

Table of Contents