70. 1. Geography Earth has a radius of about 6.4 × 10 6 6.4 times , 10 to the sixth  m. What is the approximate surface area of Earth? Use the formula for the surface area of a sphere, S . A . = 4 π r 2 . cap s . cap a . equals 4 pi , r squared , .  Write your answer in scientific notation.
    2. Oceans cover about 70% of the surface of the Earth. About how many square meters of Earth's surface are covered by ocean water?
    3. The oceans have an average depth of 3790 m. Estimate the volume of water in Earth's oceans.

C Challenge

Solve each equation. Use the fact that if a x = a y , eh to the x , equals , eh to the y , comma  then x = y . x equals y .

71. 5 6 = 25 x 5 to the sixth , equals , 25 to the x
72. 3 x = 27 4 3 to the x , equals , 27 to the fourth
73. 8 2 = 2 x 8 squared , equals , 2 to the x
74. 4 x = 2 6 4 to the x , equals , 2 to the sixth
75. 3 2 x = 9 4 3 , 2 to the x , equals , 9 to the fourth
76. 2 x = 1 32 2 to the x , equals , 1 thirty second
77. Reasoning How many different ways are there to rewrite the expression 16 x 4 16 , x to the fourth  using only the property of raising a product to a power? Show the ways.

Standardized Test Prep

SAT/ACT

78. Which expression does NOT equal 25 n 12 ? 25 , n to the twelfth , question mark

    1. ( 5 n 6 ) 2 open 5 , n to the sixth , close squared
    2. ( 5 n 3 ) ( 5 n 9 ) open 5 , n cubed , close open 5 , n to the ninth , close
    3. 25 ( n 3 ) 9 25 . open , n cubed , close to the ninth
    4. 5 2 ( n 2 ) 6 5 squared . open , n squared , close to the sixth

79. One morning an employee washed 4 cars and 2 vans in less than 115 min. That afternoon it took the employee more than 150 min to wash 3 cars and 5 vans. The information can be represented by the inequalities 4 x + 2 y < 115 4 x plus 2 y less than 115  and 3 x + 5 y > 150 , 3 x plus 5 y greater than 150 comma  where x is the time it takes to wash one car and y is the time it takes to wash one van. Which region of the graph below represents the possible numbers of minutes it takes to wash a car and a van?

    
    Image Long Description

    Washing Times

    6. A
    7. B
    8. C
    9. D

Short Response

80. A snail travels at a speed of 3 × 10 − 2 mi/h . 3 times , 10 super negative 2 end super . mislashh , .  What is the snail's speed in inches per minute? Show your work.

Mixed Review

See Lesson 7-3.

Simplify each expression.

81. b c − 6 b 3 b , c super negative 6 end super . b cubed
82. ( a 2 b 3 ) ( a 6 ) open , eh squared , b cubed , close open , eh to the sixth , close
83. 9 m 3 ( 6 m 2 n 4 ) 9 , m cubed , open 6 , m squared , n to the fourth , close
84. 2 t ( − 2 t 4 ) 2 t open negative 2 , t to the fourth , close

See Lesson 5-1.

Find the slope of the line that passes through each pair of points.

85. (0, 3), (4, 0)
86. ( 2 , − 5 ) , ( 3 , 1 ) open 2 comma negative 5 close comma open 3 comma 1 close
87. ( − 3 , 6 ) , ( 1 , 0 ) open negative 3 comma 6 close comma open 1 comma 0 close
88. ( 0 , 0 ) , ( 1 , − 9 ) open 0 comma 0 close comma open 1 comma negative 9 close

Get Ready! To prepare for Lesson 7-5, do Exercises 89–93.

See page 789.

Write each fraction in simplest form.

89. 5 20 5 twentieths
90. 124 4 124 over 4
91. 6 15 6 fifteenths
92. 5 x y 15 x fraction 5 x y , over 15 x end fraction
93. 3 a c 12 a fraction 3 eh c , over 12 eh end fraction

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