Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set: 86

Answer

$\sqrt[6] (y^{5})$

Work Step by Step

$\sqrt[3] (y^{2})\times\sqrt[6] y=y^{\frac{2}{3}}\times y^{\frac{1}{6}}$ We can further simplify by using the product rule, which holds that $a^{m}\times a^{n}=a^{m+n}$. $y^{\frac{2}{3}}\times y^{\frac{1}{6}}=y^{(\frac{2}{3}+\frac{1}{6})}=y^{(\frac{4}{6}+\frac{1}{6})}=y^{\frac{5}{6}}=\sqrt[6] (y^{5})$
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