Basic Mathematics for College Students

Use the power rule for exponents to simplify each expression.
Write the results using exponents.See Example 4.

Use the product and power rules for exponents to simplify each
expression.See Example 5.

Use the power of a product rule for exponents to simplify each
expression.See Example 6.

65. 
    
    
    
    66. 
        
    
    
    
    


66. 
    
    
    
    68. 
        
    
    
    
    


67. ( 3 a^4 b^7 )^3 70. ( 5 m^9 n^10 )^2


68. 
    
    
    
    72. 
        
    
    
    
    

Use the power of a product rule for exponents to simplify each
expression.See Example 7.

73. (2c^3 )^3 (3c^4 )^2 74. (5b^4 )^2 (3b^8 )^2


74. (10d^7 )^2 (4d^9 )^3 76. (2x^7 )^3 (4x^8 )^2

Simplify each expression.

77. (7a^9 )^2 78. (12b^6 )^2


78. t^4  t^5  t 80. n^4  n n^3


79. 
    
    
    
    82. 
        
    
    
    
    


80. 
    
    
    
    84. 
        
    
    
    
    


81. 
    
    
    
    86. 
        
    
    
    
    


82. (b^2 b^3 )^12 88. (s^3 s^3 )^3


83. (2b^4 b)^5 (3b)^2 90. (2aa^7 )^3 (3a)^3


84. (c^2 )^3 (c^4 )^2 92. (t^5 )^2 (t^3 )^3


85. (3s^4 t^3 )^3 (2st)^4 94. (2a^3 b^5 )^2 (4ab)^3


86. x x^2  x^3  x^4  x^5 96. x^10  x^9  x^8  x^7

(n^4 n)^3 (n^3 )^6 (y^3 y)^2 (y^2 )^2

( 6 a^3 b^2 )^3 ( 10 r^3 s^2 )^2

y^3 y^2 y^4 y^4 yy^6

TRY IT YOURSELF

( 2 r^2 s^3 )^3 ( 2 x^2 y^4 )^5

(5y)^4 (4t)^4

(6a)^2 (3b)^3

(u^4 )^2 (u^3 )^2 (v^5 )^2 (v^3 )^4

(t^3 )^4 (t^2 )^3 (b^2 )^5 (b^3 )^2

(p^2 p^3 )^5 (r^3 r^4 )^2

(x^2 x^3 )^5 (y^3 y^4 )^4

(y^5 )^3 (b^3 )^6

(m^50 )^10 (n^25 )^4

[(4.3)^3 ]^8 [(1.7)^9 ]^8

(3^2 )^4 (4^3 )^3

8.6 Multiplication Rules for Exponents 695

97. ART HISTORY Leonardo da Vinci’s drawing
    relating a human figure to a square and a circle is
    shown. Find an expression for the area of the square
    if the man’s height is feet.


98. PACKAGING Find an expression for the volume of
    the box shown below.


99. Explain the mistake in the following work.


100. Explain why we can simplify , but cannot
     simplify.


101. JEWELRY A lot of what we refer to as gold
     jewelry is actually made of a combination of gold
     and another metal. For example, 18-karat gold is
     gold by weight. Simplify this ratio.


102. After evaluation, what is the sign of (13)^5?


103. Divide:


104. How much did the temperature change if it went
     from 4ºF to 17ºF?


105. Evaluate:


106. Solve: 10 x 1


107. Solve:x 12


108. Divide:

0

10

2 a

12

 3

b3(5)

 25

 5

18

24

REVIEW

x^4 x^5

x^4 x^5

23  22  45 1,024

WRITING

6 x in.

6 x in.

6 x in.

5 x

APPLICATIONS