Basic Mathematics for College Students

694 Chapter 8 An Introduction to Algebra

Identify the base and the exponent in each expression.

See Example 1.

13. 
    
    
    
    14. 
        
    
    
    
    


14. 
    
    
    
    16. 
        
    
    
    
    


15. 
    
    
    
    18. 
        
    
    
    
    


16. 
    
    
    
    20. 
        
    
    
    
    


17. 
    
    
    
    22. 
        
    
    
    
    


18. 
    
    
    
    24. 
        
    
    
    
    

Write each expression in an equivalent form using an exponent.

See Example 2.

25. m m m m  m


26. r r r r r r


27. 
    


28. 
    


29. 
    


30. 
    


31. a a b b b


32. m m m  n  n

Use the product rule for exponents to simplify each expression.

Write the results using exponents.See Example 3.

33. 
    
    
    
    34. 
        
    
    
    
    


34. 
    
    
    
    36. 
        
    
    
    
    


35. 
    
    
    
    38. 
        
    
    
    
    


36. (c^5 )(c^8 ) 40. (d^4 )(d^20 )


37. 
    
    
    
    42. 
        
    
    
    
    


38. 
    
    
    
    44. 
        
    
    
    
    


39. x^2  y x y^10 46. x^3  y x y^12


40. m^100  m^100 48. n^600  n^600

cd^4 cd ab^3 ab^4

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

bb^2 b^3 aa^3 a^5

a^3 a^3 m^7 m^7

53  54 34  36

5 uuu

4 ttttt

 5 u( 5 u)( 5 u)( 5 u)( 5 u)

4 t 4 t 4 t 4 t

(y9)^4 (z2)^3

9 m^12 3.14r^4

 x^4

1

3

y^6

( 3 x)^2 (2xy)^10

a

5

x

b

3

x^5

43 (8)^2

GUIDED PRACTICE

SECTION 8.6 STUDY SET

Fill in the blank.

1. Expressions such as , and are called
   expressions.


2. Match each expression with the proper description.

a. Product of exponential expressions with the same

base

b. Power of an exponential expression

c. Power of a product

Fill in the blanks.

3. a.
   b.


4. a. b.
   c. d.


5. To simplify each expression, determine whether you
   add, subtract, multiply, or divide the exponents.
   a.
   b.
   c.


6. To simplify , what factors within the
   parentheses must be raised to the fourth
   power?

Simplify each expression, if possible.

7. a. b.


8. a. b.


9. a. b.


10. a. b.

Complete each solution to simplify each expression.

11.

12. (x^4 )^3 (x^2 )^3
    x^12 x^6
    x

x

x

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

NOTATION

42  24 x^3 y^2

x^3 x^2 x^3 x^2

x^2 x x^2 x

x^2 x^2 x^2 x^2

(2y^3 z^2 )^4

(a^4 b^2 )^5

(n^8 )^4

b^6 b^9

(xy)n (ab)c

xx xmxn

( 5 y)( 5 y)( 5 y)

(3x)^4    

CONCEPTS

(a^4 b^2 )^5 (a^8 )^4 a^5 a^3

x^4 , 10^3 (5t)^2

VOCABULARY