Intermediate Algebra (11th edition)

274 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions

Complete solution available
on the Video Resources on DVD

5.1 EXERCISES

Concept Check Decide whether each expression has been simplified correctly. If not, cor-

rect it.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   5. 
      
      
      
      6. 7.Concept Check Your friend evaluated as. WHAT WENT WRONG?Give
         the correct answer.
         8.Concept Check Another friend evaluated as , or 8. WHAT WENT WRONG?Give
         the correct answer.
      
      
      
      
   
   
   
   

Apply the product rule for exponents, if possible, in each case. See Example 1.

9. 
   
   
   
   10. 
       
       
       
       11. 
           
           
           
           12. 
               
           
           
           
           
       
       
       
       
   
   
   
   


10. 
    
    
    
    14. 
        
        
        
        15. 
            
            
            
            16. 
                
            
            
            
            
        
        
        
        
    
    
    
    


11. 
    
    
    
    18. 
        
        
        
        19. 
            
            
            
            20. 
                
            
            
            
            
        
        
        
        
    
    
    
    

In Exercises 21 and 22, match the expression in Column I with its equivalent expression in

Column II. Choices may be used once, more than once, or not at all.*See Example 2.

III III

21. (a) A. 0
    (b) B. 1
    (c) C.
    (d) D. 9
    E. - 9

- 1 - 920

1 - 920 - 1

- 90

90

12 x^2 y^5219 xy^3218 s^4 t 213 s^3 t^52 r^2 #s^4 p^3 #q^2

x^3 #x^5 #x^9 y^4 #y^5 #y^61 - 3 w^5219 w^321 - 5 x^2213 x^42

134 # 138 116 # 114 89 # 8 12 # 126

(^623)
5
32
45 # 42 167
y^2 #y^4 =y^8 x^3 #x^4 =x^7 xy^0 = 0 1 yZ 02
a 1 aZ 02

3

a

b

4

=

34

a

1 ab 22 =ab^215 x 23 = 53 x^3

*The authors thank Mitchel Levy of Broward College for his suggestions for these exercises.

22. (a) A. 0
    (b) B. 1
    (c) C.
    (d) D. 8
    E. - 8

1 - 8 x 20

18 x 20 - 1

• 8 x^0

8 x^0

Evaluate. Assume that all variables represent nonzero real numbers.*See Example 2.

23. 
    
    
    
    24. 
        
        
        
        25. 
            
            
            
            26. 
                
            
            
            
            
        
        
        
        
    
    
    
    


24. 
    
    
    
    28. 
        
        
        
        29. 
            
            
            
            30. 
                
            
            
            
            
        
        
        
        
    
    
    
    


25. 
    
    
    
    32. 
        
        
        
        33. 
            
            
            
            34. 
                
            
            
            
            
        
        
        
        
    
    
    
    

In Exercises 35 and 36, match the expression in Column I with its equivalent expression in

Column II. Choices may be used once, more than once, or not at all.* See Example 3.

III III

35. (a) A. 25

(b) B.

(c) C.

(d) D.-

1

25

- 1 - 52 -^2

1 - 52 -^2 - 25

1

25

- 5 -^2

5 -^2

• 30 + 30 - 50 + 50 - 40 - m^0 - 80 - k^0

1 - 2520 1 - 3020 30 + 1 - 320 50 + 1 - 520

150 190 - 80 - 100

36. (a) A. 64
    (b) B.

(c) C.

(d) D.-

1

64

- 1 - 42 -^3

1

64

1 - 42 -^3

- 4 -^3 - 64

4 -^3

Write each expression with only positive exponents. Assume that all variables represent

nonzero real numbers. In Exercises 49 –52, simplify each expression. See Example 3.

37. 
    
    
    
    38. 
        
        
        
        39. 
            
            
            
            40. 
                
            
            
            
            
        
        
        
        
    
    
    
    


38. 14 x 2 -^2 42. 15 t 2 -^3 43. 4 x-^2 44. 5 t-^3

5 -^47 -^29 -^114 -^1