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 7.4 - Adding, Subtracting, and Dividing Radical Expressions - Exercise Set: 41

Answer

$\dfrac{\sqrt[4]{9y^6}}{x^2}$

Work Step by Step

RECALL: The quotient rule: $\sqrt[n]{\dfrac{a}{b}}=\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$ where $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$ Use the quotient rule above to obtain: $=\dfrac{\sqrt[4]{9y^6}}{\sqrt[4]{x^{8}}}$ Factor the radicand of the denominator so that at least one factor is a perfect fourth power to obtain: $=\dfrac{\sqrt[4]{9y^6}}{\sqrt[4]{(x^2)^4}}$ Simplify to obtain; $=\dfrac{\sqrt[4]{9y^6}}{x^2}$
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