Beginning Algebra, 11th Edition

OBJECTIVE 4 Use combinations of rules.

Using Combinations of Rules

Simplify. Assume that all variables represent nonzero real numbers.

(a)

Power rule (a)

Quotient rule

= 4

= 41

= 46 -^5

=

46

45

14223

45

EXAMPLE 5

308 CHAPTER 5 Exponents and Polynomials

NOW TRY
EXERCISE 5
Simplify. Assume that all
variables represent nonzero
real numbers.

(a) (b)

(c) (d)

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

12 ab^3 c-^425

a

7 y^4

10

b

• 3

14 t 2514 t 2 -^3

315

(^13324) (b)
Product rule
Power rule (b)

= 32 x^5

= 25 x^5

= 12 x 25

12 x 2312 x 22

(c)

Power rules (a)–(c)

=

625

16 x^12

=

54

24 x^12

= a

5

2 x^3

b

4

a

2 x^3

5

b

• 4

(e)

Power rule (b)

Negative-to-positive rule

Quotient rule

or NOW TRY

81 m

64

=

34 m

43

,

=

34 m^4 -^3

43

=

34 m^4

43 m^3

=

4 -^3 m-^3

3 -^4 m-^4

14 m 2 -^3

13 m 2 -^4

(d)

Power rules (a)–(c)

=

x^6 y^9

1728

=

x^6 y^9

43 # 33

=

3 -^3 x^6

43 y-^9

a

3 x-^2

4 -^1 y^3

b

• 3

Negative-to-

positive rule

Negative-to-

positive rule

NOW TRY ANSWERS

5. (a) (b)

(c) (d) c

17

32 a^11 b^9

1000

343 y^12

33 , or 27 16 t^2

Complete solution available
on the Video Resources on DVD

5.2 EXERCISES

Decide whether each expression is equal to 0, 1,or. See Example 1.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   6. 
      
      
      
      7. 
         
         
         
         8. 
            
         
         
         
         
      
      
      
      
   
   
   
   

9. 10. 11. 12.

05

20

010

120

1 - 420 - 40 1 - 1120 - 110

- 80 - 60 - 1 - 620 - 1 - 1320

90 30 1 - 220 1 - 1220

- 1

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