Name Date
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.
- 49
3
(^2) 2. 16
1
(^4) 3. 125 −
2
(^3) 4. 100
3
2
- 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.