Intermediate Algebra (6th Edition)

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

Chapter 7 - Sections 7.1-7.5 - Integrated Review - Radicals and Rational Exponents: 15

Answer

$x^{\frac{5}{4}}$

Work Step by Step

We can use the product rule to simplify, which holds that $a^{m}\times a^{n}=a^{m+n}$ (where a is a real number, and m and n are positive integers). $\frac{x^{\frac{1}{4}}x^{\frac{3}{4}}}{x^{-\frac{1}{4}}}=\frac{x^{\frac{1}{4}+\frac{3}{4}}}{x^{-\frac{1}{4}}}=\frac{x^{\frac{4}{4}}}{x^{-\frac{1}{4}}}$ Next, we can use the quotient rule, which holds that $\frac{a^{m}}{a^{n}}=a^{m-n}$ (where a is a nonzero real number, and m and n are integers). $x^{\frac{4}{4}-(-\frac{1}{4}})=x^{\frac{5}{4}}$
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