Beginning Algebra, 11th Edition

SECTION 5.1 The Product Rule and Power Rules for Exponents^301

NOW TRY
EXERCISE 8
Write an expression that
represents the area of the
figure. Assume x 7 0.

(a)For FIGURE 1, use the formula for the area of a rectangle,

Area formula

Commutative property; product rule

Multiply. Add the exponents.

(b)FIGURE 2is a triangle with base and height

Area formula

Substitute.

a= Product rule; multiply. NOW TRY

1

2

118 m^72 , or 9 m^7

a=

1

2

16 m^4213 m^32

a=

1

2

bh

6 m^43 m^3.

a= 30 x^7

a= 6 # 5 #x^4 +^3

a= 16 x^4215 x^32

a=LW.

10 x^8

3 x^7

NOW TRY ANSWER

8. 15 x^15

Complete solution available
on the Video Resources on DVD

5.1 EXERCISES

Concept Check Decide whether each statement is trueor false. If false, tell why.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
         
         
         
         
      
      
      
      
   
   
   
   

Write each expression by using exponents. See Example 1.

5. 
   
   
   
   6. 
      
   
   
   
   


6. 
   
   
   
   8. 
      
   
   
   
   


7. 
   
   
   
   10. 
       
   
   
   
   


8. 
   
   
   
   12. 13.Explain how the expressions and are different.
       14.Explain how the expressions and are different.
   
   
   
   

Identify the base and the exponent for each exponential expression. In Exercises 15–18, also

evaluate each expression. See Example 2.

15. 
    
    
    
    16. 
        
        
        
        17. 
            
            
            
            18. 
                
            
            
            
            
        
        
        
        
    
    
    
    


16. 
    
    
    
    20. 
        
        
        
        21. 
            
            
            
            22. 23.Explain why the product rule does not apply to the expression. Then evaluate the
                expression by finding the individual powers and adding the results.
                24.Repeat Exercise 23for the expression.
            
            
            
            
        
        
        
        
    
    
    
    

Use the product rule, if possible, to simplify each expression. Write each answer in exponen-

tial form. See Example 3.

25. 
    
    
    
    26. 
        
        
        
        27. 
            
        
        
        
        
    
    
    
    


26. 
    
    
    
    29. 
        
        
        
        30. 
            
        
        
        
        
    
    
    
    


27. 
    
    
    
    32. 
        
        
        
        33. 
            
        
        
        
        
    
    
    
    


28. 
    
    
    
    35. 
        
        
        
        36. 
            
        
        
        
        
    
    
    
    


29. 
    
    
    
    38. 
        
        
        
        39. 
            
        
        
        
        
    
    
    
    


30. 412 + 45 41. 58 # 39 42. 63 # 89

15 x^221 - 2 x^3213 x^42112 y^3214 y 21 - 3 y^5238 + 39

110 a^721 - 4 a^321 - 6 p^521 - 7 p^521 - 5 w^821 - 9 w^82

t^3 #t^8 #t^13 n^5 #n^6 #n^91 - 8 r^4217 r^32

53 # 58 # 52 1 - 7231 - 726 1 - 9281 - 925

52 # 56 36 # 37 42 # 47 # 43

1 - 423 + 1 - 424

52 + 53

1 - 6 x 24 1 - 8 x 24 - 6 x^4 - 8 x^4

35 27 1 - 325 1 - 227

15 x 23 5 x^3

1 - 324 - 34

1 - 7 y 21 - 7 y 21 - 7 y 21 - 7 y 2 1 - 8 p 21 - 8 p 21 - 8 p 21 - 8 p 21 - 8 p 2

1 - 421 - 421 - 421 - 42 1 - 321 - 321 - 321 - 321 - 321 - 32

a

1

4

ba

1

4

ba

1

4

ba

1

4

ba

1

4

a b

1

2

ba

1

2

ba

1

2

ba

1

2

ba

1

2

ba

1

2

b

w#w#w#w#w#w t#t#t#t#t#t#t

a

1

5

b

2

=

1

52

33 = 9 1 - 324 = 34 1 x^223 =x^5