# Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set - Page 430: 30

$\dfrac{3x\sqrt[3]{3}}{2}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\dfrac{3}{4}\sqrt[3]{24x^3} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3}{4}\sqrt[3]{8x^3\cdot3} \\\\= \dfrac{3}{4}\sqrt[3]{(2x)^3\cdot3} \\\\= \dfrac{3}{4}\cdot2x\sqrt[3]{3} \\\\= \dfrac{3}{\cancel{2}(2)}\cdot\cancel{2}x\sqrt[3]{3} \\\\= \dfrac{3x\sqrt[3]{3}}{2} .\end{array} Note that all variables are assumed to have positive values.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.