Simplify each expression.

60. 3 n 2 ( 5 0 ) 2 n 3 fraction 3 , n squared . open , 5 to the , close , over 2 , n cubed end fraction
61. ( 2 m 4 m 2 ) − 4 open . fraction 2 , m to the fourth , over m squared end fraction . close super negative 4 end super
62. 3 x 3 ( 3 x ) 3 fraction 3 , x cubed , over open , 3 x , close cubed end fraction
63. ( 2 a 6 ) ( 4 a ) 8 a 3 fraction open , 2 , eh to the sixth , close . open , 4 eh , close , over 8 , eh cubed end fraction
64. ( 9 t 2 36 t ) 3 open . fraction 9 , t squared , over 36 t end fraction . close cubed
65. ( a 4 a a 2 ) − 3 open . fraction eh to the fourth , eh , over eh squared end fraction . close super negative 3 end super
66. ( 2 x 2 5 x 3 ) − 2 open . fraction 2 , x squared , over 5 , x cubed end fraction . close super negative 2 end super
67. 4 x x − 2 y 4 8 x 3 ( y − 2 ) 3 fraction 4 . x super x minus 2 end super . y to the fourth , over 8 , x cubed . open , y super negative 2 end super , close cubed end fraction
68. 1. Open-Ended Write three numbers greater than 1000 in scientific notation.
    2. Divide each number by 2.
    3. Reasoning Is the exponent of the power of 10 divided by 2 when you divide a number in scientific notation by 2? Explain.
69. Simplify the expression ( 3 x 2 ) − 3 open , fraction 3 , over x squared end fraction , close super negative 3 end super  in three different ways. Justify each step.

70. Geometry The area of the rectangle is 72 a 3 b 4 . 72 , eh cubed , b to the fourth , .  What is the length of the rectangle?

    

    1. a 3 b 4 12 fraction eh cubed , b to the fourth , over 12 end fraction
    2. 12 a 2 b 3 12 , eh squared , b cubed
    3. 12 a 3 b 4 fraction 12 , over eh cubed , b to the fourth end fraction
    4. 12 a 3 b 4 12 , eh cubed , b to the fourth

Simplify each expression.

71. ( 3 x y 5 x 4 y ) − 2 open . fraction 3 x , y to the fifth , over x to the fourth , y end fraction . close super negative 2 end super
72. m 4 n 3 p − 3 m − 2 n 7 p − 8 fraction m to the fourth , n cubed . p super negative 3 end super , over m super negative 2 end super . n to the seventh . p super negative 8 end super end fraction
73. ( 1 4 ) − 2 ( 1 6 ) − 3 fraction open , 1 fourth , close super negative 2 end super , over open , 1 sixth , close super negative 3 end super end fraction
74. 0.2 3 ⋅ 0.2 4 0.2 7 fraction 0.2 cubed , dot , 0.2 to the fourth , over 0.2 to the seventh end fraction
75. ( a − 1 b 3 c a 2 b 4 ) 6 open . fraction eh super negative 1 end super . b cubed , c , over eh squared , b to the fourth end fraction . close to the sixth
76. ( ( − 4 ) 2 ( − 3 ) − 3 ) 2 open . fraction open , negative 4 , close squared , over open , negative 3 , close super negative 3 end super end fraction . close squared
77. ( ( 4 x ) 2 y x y 4 ) − 2 open . fraction open , 4 x , close squared . y , over x , y to the fourth end fraction . close super negative 2 end super
78. ( 6 a 3 ) ( 8 b 4 ) ( 2 a 4 ) ( 36 b − 1 ) fraction open , 6 , eh cubed , close . open , 8 , b to the fourth , close , over open , 2 , eh to the fourth , close . open . 36 , b super negative 1 end super . close end fraction

79. Physics The wavelength of a radio wave is defined as speed divided by frequency. An FM radio station has a frequency of 9 × 10 7 9 times , 10 to the seventh  waves per second. The speed of the waves is about 3 × 10 8 3 times , 10 to the eighth  meters per second. What is the wavelength of the station?

80. 

    1. Error Analysis What mistake did the student make in simplifying the expression above?
    2. What is the correct simplified form of the expression?

81. Writing Suppose a x a y = a 3 fraction eh to the x , over eh to the y end fraction . equals , eh cubed  and a x a 3 y = a − 5 . fraction eh to the x , over eh super 3 y end super end fraction . equals , eh super negative 5 end super . .  Find the values of x and y. Explain how you found your answer.

82. 1. Finance In 2000, the United States government owed about $5.63 trillion to its creditors. The population of the United States was 282.4 million people. How much did the government owe per person in 2000? Round to the nearest dollar.
    2. In 2005, the debt had grown to $7.91 trillion, with a population of 296.9 million. How much did the government owe per person? Round to the nearest dollar.
    3. What was the percent increase in the average amount owed per person from 2000 to 2005?

Write each expression with only one exponent. You may need to use parentheses.

83. m 7 n 7 fraction m to the seventh , over n to the seventh end fraction
84. 10 7 ⋅ 10 0 10 − 3 fraction 10 to the seventh , dot , 10 to the , over 10 super negative 3 end super end fraction
85. 27 x 3 8 y 3 fraction 27 , x cubed , over 8 , y cubed end fraction
86. 4 m 2 169 m 4 fraction 4 , m squared , over 169 , m to the fourth end fraction

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