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 7.3 - Multiplying and Simplifying Radical Expressions - Exercise Set - Page 531: 75


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

Work Step by Step

Apply product rule: $\sqrt[n] p \sqrt[n] q=\sqrt[n]{pq}$ Here, $n$ refers as index. $\sqrt[3] {25x^4y^2} \sqrt[3] {5xy^{12}}=\sqrt {(25x^4y^2) (5xy^{12})}= \sqrt[3]{125x^5y^{14}}$ The radical $\sqrt[3]{125x^5y^{14}}$ can be further simplified by using product rule again. Such as: $\sqrt[3]{125x^5y^{14}}=\sqrt[3] {(5xy^4)^3 (x^2y^2)}=\sqrt[3] {(5xy^4)^3} \sqrt[3]{ (x^2y^2)}=5xy^4 \sqrt[3] {x^2y^2}$
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