Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 49

$\dfrac{\sqrt[3]{75ac^2}}{5c}$

Rationalizing the denominator of the given expression, $ \dfrac{\sqrt[3]{3a}}{\sqrt[3]{5c}} ,$ we find: \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{3a}}{\sqrt[3]{5c}}\cdot\dfrac{\sqrt[3]{25c^2}}{\sqrt[3]{25c^2}} \\\\= \dfrac{\sqrt[3]{75ac^2}}{\sqrt[3]{125c^3}} \\\\= \dfrac{\sqrt[3]{75ac^2}}{\sqrt[3]{(5c)^3}} \\\\= \dfrac{\sqrt[3]{75ac^2}}{5c} .\end{array}