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: 22

Answer

$\sqrt[5]{y^2} \text{ or } \left(\sqrt[5]{y}\right)^2$

Work Step by Step

We are asked to rewrite the exponent into radical form: $y^{\frac{2}{5}}$ Recall the rational exponent property (pg. 382): $a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$ Applying this property to our equation ($m=2$, $n=5$, $a=y$), we get: $y^{\frac{2}{5}}=\sqrt[5]{y^2}=(\sqrt[5]{y})^2$
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