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: 102

Answer

$\sqrt[10]{y}$

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 rule (3) above to obtain: $=\dfrac{y^{\frac{2}{5}}}{y^{\frac{3}{10}}}$ Use rule (2) above to obtain: $=y^{\frac{2}{5}-\frac{3}{10}}$ Make the fractions similar using their LCD of $10$ to obtain: $=y^{\frac{4}{10} - \frac{3}{10}} \\=y^{\frac{4-3}{10}} \\=y^{\frac{1}{10}}$ Use rule (1) above to obtain: $=\sqrt[10]{y}$
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