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: 99

Answer

$\sqrt[20]{x}$

Work Step by Step

RECALL: (1) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ Use rule (1) above to obtain: $=\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{5}}}$ Use rule (2) above to obtain: $=x^{\frac{1}{4}-\frac{1}{5}}$ Make the fractions similar using their LCD of $20$ to obtain: $=x^{\frac{5}{20} - \frac{4}{20}} \\=x^{\frac{5-4}{20}} \\=x^{\frac{1}{20}}$ Use rule (1) above to obtain: $=\sqrt[20]{x}$
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