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

(Marvins-Underground-K-12) #1
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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:


  1. 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.



  2. 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.



  1. 4


√ 2
· 4

√ 2


  1. (3


√ 2
)

√ 2
3.

5

√ 2

52


  1. 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
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©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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