Answer
$9$
Work Step by Step
When raising a power to a power, multiply the two powers together:
$3^{(2 + \sqrt 2)(2 - \sqrt 2)}$
Use formula $(a+b)(a-b)=a^2-b^2$ in the exponent:
$3^{2^2-(\sqrt2)^2}\\
=3^{4-2}\\
=3^2\\
=9$
Algebra 2 Common Core
by Hall, Prentice
Published by
Prentice Hall
ISBN 10:
0133186024
ISBN 13:
978-0-13318-602-4
Chapter 6 - Radical Functions and Rational Exponents - 6-4 Rational Exponents - Practice and Problem-Solving Exercises - Page 388: 96
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