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: 52

Answer

$x^2y^2$

Work Step by Step

RECALL: The quotient rule: $\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}}$ where $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$ Use the rule above to obtain: $\require{cancel}=\sqrt{\dfrac{x^7y^6}{x^3y^2}} \\=\sqrt{\dfrac{x^4\cancel{x^7}\cancel{y^6}y^4}{\cancel{x^3y^2}}} \\=\sqrt{x^4y^4} \\=\sqrt{(x^2y^2)^2}$ Simplify to obtain: $=x^2y^2$
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