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

Name Date

WORKSHEET 8.14: USING RATIONAL NUMBERS AS

EXPONENTS

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

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

5. 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.