The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 6.1: USING ZERO AND NEGATIVE NUMBERS AS

EXPONENTS

-------------------------------------------------------------------------------------

Examine the table below to discover patterns involving 3 n. The numbers in the top row

represent exponents of 3. Because the base is 3, each term is

1

3

of the previous term.

n 3 210− 1 − 2 − 3

----------------------------------------------------------------------------------------

3 n 27931

1

3

1

9

1

27

Following is the definition of zero as an exponent. Ifxis a nonzero number, thenx^0 = 1.

EXAMPLES

40 =1(−2)^0 = 1

(

1

5

) 0

= 1

Following are the definitions of negative exponents. Ifxis a nonzero number, thenx−n=

1

xn

and

1

x−n

=xn

EXAMPLES

4 −^2 =

1

42

=

1

16

1

5 −^2

= 52 = 25

DIRECTIONS: Simplify each expression.

1. 
   

   5 −^2 2. 60 3.(−3)−^4 4.− 3 −^4

   
   


2. 
   

(

2

3

) 0

6. 
   

1

7 −^2

7.− 4 −^2 8.(−4)−^2

9. 
   

(

3

8

)− 1

10. 
    

1

6 −^2

11. (−2)−^3 12. 2 −^3

CHALLENGE:Is− 50 the same as (−5)^0 .Explainyouranswer.

225

Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.