Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 8 - Radical Functions - 8.3 Multiplying and Dividing Radicals - 8.3 Exercises - Page 643: 89

Answer

$\frac{2\sqrt[3] {12mn^2}}{55mn}$.

Work Step by Step

The given expression is $=\frac{4\sqrt[3] {6m^2n}}{55\sqrt[3]{4m^4n^2}}$ Use division rule. $=\frac{4}{55}\cdot \sqrt[3] {\frac{6m^2n}{4m^4n^2}}$ Reduce the fraction. $=\frac{4}{55}\cdot \sqrt[3] {\frac{3}{2m^2n}}$ Multiply by the needed factors. $=\frac{4}{55}\cdot \sqrt[3] {\frac{3}{2m^2n}}\cdot \sqrt[3] {\frac{2^2mn^2}{2^2mn^2}}$ Use multiplication rule. $=\frac{4}{55}\cdot \sqrt[3] {\frac{3\cdot 2^2mn^2}{2m^2n\cdot 2^2mn^2}}$ Simplify. $=\frac{4}{55}\cdot \sqrt[3] {\frac{12mn^2}{2^3m^3n^3}}$ Cube root the denominator. $=\frac{4}{55}\cdot \frac{\sqrt[3] {12mn^2}}{2mn}$ Simplify. $=\frac{2\sqrt[3] {12mn^2}}{55mn}$.
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