Algebra 2 Common Core

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 386: 17

Answer

$3$

Work Step by Step

The given expression is equivalent to: $=3^{\frac{1}{3}}\left(3\cdot3\right)^{\frac{1}{3}}$ Recall the basic exponent property (pg. 360): $(ab)^n=a^nb^n$ Applying this property, the expression above becomes: $=3^{\frac{1}{3}}\cdot 3^{\frac{1}{3}}\cdot 3^{\frac{1}{3}}$ Recall the basic exponent property (pg. 360): $a^ma^n=a^{m+n}$ Applying this property, the expression above simplifies to: $=3^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}$ $=3^{1}$ $=3$
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