Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-5 Rational Exponents and Radicals - Got It? - Page 450: 3


$a.\quad s^{2/3}$ $b.\quad 12\cdot x^{4/3}$ $c.\quad 32y^{5/2}$ $d.\quad 4a^{2}$

Work Step by Step

Apply the key concept: $\sqrt[n]{a^{m}}=a^{m/n}$ $a.$ $\sqrt[3]{s^{2}}=s^{2/3}$ $b.$ $12\sqrt[3]{x^{4}}=12\cdot x^{4/3}$ $c.$ $\sqrt[2]{(4y)^{5}}=(4y)^{5/2}=4^{5/2}y^{5/2}=(2^{2})^{5/2}=2^{5}y^{5/2}=32y^{5/2}$ $d.$ Recognize that $256=2^{8}=4^{4}$ $\sqrt[4]{256a^{8}}=\sqrt[4]{4^{4}(a^{2})^{4}}=\sqrt[4]{(4a^{2})^{4}}=4a^{2}$
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