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 - Review Exercises - Page 577: 38

Answer

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

Work Step by Step

Simplify . $\sqrt[3]{54x^8y^6}$ As per the product rule, we have $\sqrt[n] {pq}=\sqrt[n] {p}\sqrt[n] {q}$ $\sqrt[3]{54x^8y^6}=\sqrt[3] {54}\sqrt[3] {x^8}\sqrt[3] {y^6}$ Thus, $=\sqrt[3] {3^3}\sqrt[3] {(x^2)^6}\sqrt[3] {(y^2)^3} \sqrt[3]{2x^2}$ or, $=\sqrt[3]{(3x^2y^2)^3} \sqrt[3]{2x^2}$ Hence, the above exponent in radical form can be written as: or, $3x^2y^2 \sqrt[3]{2x^2}$
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