Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set: 101

Answer

$\sqrt{y}$

Work Step by Step

RECALL: (1) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ (3) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ Use rules (1) and (3) above to obtain: $=\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{6}}}$ Use rule (2) above to obtain: $=y^{\frac{2}{3}-\frac{1}{6}}$ Make the fractions similar using their LCD of $6$ to obtain: $=y^{\frac{4}{6} - \frac{1}{6}} \\=y^{\frac{4-1}{6}} \\=y^{\frac{3}{6}} \\=y^{\frac{1}{2}}$ Use rule (1) above to obtain: $=\sqrt{y}$
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