Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 19

$\dfrac{3a\sqrt[3]{a}}{2b}$

Work Step by Step

Using the properties of radicals, the given expression, $\sqrt[3]{\dfrac{27a^4}{8b^3}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{27a^4}}{\sqrt[3]{8b^3}} \\\\= \dfrac{\sqrt[3]{27a^3\cdot a}}{\sqrt[3]{8b^3}} \\\\= \dfrac{\sqrt[3]{(3a)^3\cdot a}}{\sqrt[3]{(2b)^3}} \\\\= \dfrac{3a\sqrt[3]{a}}{2b} \end{array} * Note that it is assumed that all variables represent positive numbers.

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