Name Date
WORKSHEET 8.15: USING IRRATIONAL NUMBERS AS
EXPONENTS
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The properties of exponents that apply to expressions with rational exponents also apply to
expressions with irrational exponents. Follow the guidelines below to simplify expressions
with irrational exponents:
- If the bases are the same:
- To multiply two expressions, add the exponents.
- To raise a power to a power, multiply the exponents.
- To divide two expressions, subtract the exponent in the denominator from the expo-
nent in the numerator.
- If the bases are different, express each number in terms of the same base. Then follow
the guidelines for the bases being the same.
EXAMPLES
8
√ 2
· 8
√ 3
= 8
√ 2 +√ 3
49
√
(^2) · 72 =(7 (^2) )
√
(^2) · 72 = 72
√
(^2) · 72 = 72
√
2 + 2
8
√ 2
16
√ 3 =
(2^3 )
√ 2
(2^4 )
√ 3 = 23
√
2 − 4 √ 3
DIRECTIONS: Simplify.
- 4
√ 2
· 4
√ 2
- (3
√ 2
)
√ 2
3.
5
√ 2
52
- 82 · 4
√
(^2) 5.^36
√ 7
62
6.
252
125
√
2
CHALLENGE:Leah simplified 3
√
(^2) · 9
√
(^2) as 9 2
√
(^2). Is she correct? Explain your
answer.
303
Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.