Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.2 - Simplifying Radicals - Problem Set 9.2: 50

Answer

$x\sqrt[3]{3}$

Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{1}{3}\sqrt[3]{81x^3} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{3}\sqrt[3]{27x^3\cdot3} \\\\= \dfrac{1}{3}\sqrt[3]{(3x)^3\cdot3} \\\\= \dfrac{1}{3}\cdot3x\sqrt[3]{3} \\\\= \dfrac{1}{\cancel{3}}\cdot\cancel{3}x\sqrt[3]{3} \\\\= x\sqrt[3]{3} .\end{array} Note that all of the variables are assumed to represent non-negative real numbers.
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