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: 43

Answer

$\dfrac{2x^2\sqrt[5]{2x^3}}{y^4}$

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: $=\dfrac{\sqrt[5]{64x^{13}}}{\sqrt[5]{y^{20}}}$ Factor each radicand so that at least one factor is a perfect fifth power to obtain: $=\dfrac{\sqrt[5]{32x^{10}(2x^3)}}{\sqrt[5]{(y^4)^5}} \\=\dfrac{\sqrt[5]{(2x^2)^5(2x^3)}}{\sqrt[5]{(y^4)^5}}$ Simplify to obtain: $=\dfrac{2x^2\sqrt[5]{2x^3}}{y^4}$
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