Beginning Algebra, 11th Edition

Simplify by writing each expression with positive exponents. Assume that all variables repre-

sent nonzero real numbers. See Example 5.

63. 
    
    
    
    64. 
        
        
        
        65. 
            
            
            
            66. 
                
            
            
            
            
        
        
        
        
    
    
    
    

67. 68. 69. 70.

71. 72. 73. 74.

75. 76. 77. 78.

Brain Busters Simplify by writing each expression wth positive exponents. Assume that all

variables represent nonzero real numbers.

79. 
    
    
    
    80. 
        
    
    
    
    

81. 82.

83. 84.

85.Concept Check A student simplified as shown.

WHAT WENT WRONG?Give the correct answer.

86.Concept Check A student simplified as shown.

WHAT WENT WRONG?Give the correct answer.

- 54 = 1 - 524 = 625

- 54

163

22

=a

16

2

b

3 - 2

= 81 = 8

163

22

14 -^1 a-^1 b-^22 -^215 a-^3 b^42 -^2

13 a-^3 b-^522

19 -^1 z-^2 x 2 -^114 z^2 x^42 -^2

15 z-^2 x-^322

13 p-^2 q^32215 p-^1 q-^42 -^1

1 p^2 q-^22 -^3

12 y-^1 z^22213 y-^2 z-^323

1 y^3 z^22 -^1

1 m^6 n 2 -^21 m^2 n-^223

m-^1 n-^2

14 a^2 b^32 -^212 ab-^123

1 a^3 b 2 -^4

a

wz-^5

w-^3 z

b

• 2
  a

xy-^2

x^2 y

b

1 a-^2 b-^3 c-^42 -^5 -^3

1 a^2 b^3 c^42 -^4

1 x-^1 y^2 z 2 -^2

1 x-^3 y^3 z 2 -^1

1 m^8 n-^422

m-^2 n^5

1 m^7 n 2 -^2

m-^4 n^3

16 x 2416 x 2 -^3110 y 29110 y 2 -^8

a

p-^4 q

r-^3

b

• 3
  a

x-^1 y

z^2

b

12 y 2 -^3 -^2

15 y 2 -^4

13 x 2 -^2

14 x 2 -^3

x-^3 #x^5 #x-^4 y-^8 #y^5 #y-^2

15322

52

17423

79

310 CHAPTER 5 Exponents and Polynomials

Evaluate.

87. 
    
    
    
    88. 
        
        
        
        89. 
            
            
            
            90. 
                
            
            
            
            
        
        
        
        
    
    
    
    


88. 38 , 10 92. 6504 , 100 93. 277 , 1000 94. 49 ,10,000

10164282 1001 72.79 2 10001 1.53 2 10,000 1 36.94 2

PREVIEW EXERCISES

EXERCISES 59–62

FOR INDIVIDUAL OR GROUP WORK

In Objective 1,we showed how acts as 1 when it is applied to the product rule, thus

motivating the definition of 0 as an exponent. We can also use the quotient rule to

motivate this definition. Work Exercises 59–62 in order.

59.Consider the expression. What is its simplest form?

60.Because , the expression can be written as the quotient of powers of 5.

Write the expression in this way.

61.Apply the quotient rule for exponents to the expression you wrote in Exercise 60.

Give the answer as a power of 5.

62.Your answers in Exercises 59 and 61must be equal because they both represent.

Write this equality. What definition does this result support?

25

25

25

25 = (^525)
2
25
25

60

RELATING CONCEPTS

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