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

Name Date

WORKSHEET 8.15: USING IRRATIONAL NUMBERS AS

EXPONENTS

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

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

2. (3

√ 2

)

√ 2

3.

5

√ 2

52

4. 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.