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

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WORKSHEET 8.14: USING RATIONAL NUMBERS AS
EXPONENTS
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Follow the rules below when simplifying expressions that have rational numbers as
exponents:
If the rational exponent is positive,x

m
n =(√nx)m:


  • The denominator of the exponent indicates the root of the number. Write the base using
    the denominator as the index and evaluate the expression.

  • Multiply the expression the number of times the base is used as a factor. The numera-
    torindicatesthenumberoftimesthebaseisusedasafactor.


If the rational exponent is negative,x−

m
n=^1
x

m
n

=

1

(n


x)m

:


  • Place ‘‘1’’ over the expression, which makes the exponent positive.

  • Then follow the steps above.


EXAMPLES


27

2

(^3) =(^3



27)^2 = 32 = 927 −

2

(^3) =^1
27
2
3


=

1

(^3


27)^2

=

1

9

DIRECTIONS: Simplify each expression.



  1. 49


3

(^2) 2. 16
1
(^4) 3. 125 −
2
(^3) 4. 100
3
2



  1. 64 −


1

(^2) 6. 1000 −
2
(^3) 7. 16
3
(^2) 8. 216
− 2
3
CHALLENGE:Victor simplified 16
4
(^2) as (

16)^4 or 4^4 , which equals 256. Ben
rewrote the exponent
4
2
as 2 and then said that16^2 =256. Are both
methods correct? Explain your answer.
301
Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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