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: 76

Answer

$5$

Work Step by Step

RECALL: (1) $a^m \cdot a^n = a^{m+n}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ Use rule (1) above to obtain: $=\dfrac{5^{\frac{3}{4}+\frac{1}{2}}}{5^{\frac{1}{4}}} \\=\dfrac{5^{\frac{3}{4}+\frac{2}{4}}}{5^{\frac{1}{4}}} \\=\dfrac{5^{\frac{3+2}{4}}}{5^{\frac{1}{4}}} \\=\dfrac{5^{\frac{5}{4}}}{5^{\frac{1}{4}}}$ Use rule (2) above to obtain: $=5^{\frac{5}{4} - \frac{1}{4}} \\=5^{\frac{5-1}{4}} \\=5^{\frac{4}{4}} \\=5^{1} \\=5$
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