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

(Marvins-Underground-K-12) #1
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WORKSHEET 6.1: USING ZERO AND NEGATIVE NUMBERS AS
EXPONENTS
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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
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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

3

) 0





1

7 −^2

7.− 4 −^2 8.(−4)−^2






(

3

8

)− 1





1

6 −^2


  1. (−2)−^3 12. 2 −^3


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

225

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

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