Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set - Page 718: 51

$\dfrac{\sqrt[3]{5y^{2}}}{\sqrt[3]{4x}}=\dfrac{5y}{\sqrt[3]{100xy}}$

$\dfrac{\sqrt[3]{5y^{2}}}{\sqrt[3]{4x}}$ Multiply this expression by $\dfrac{\sqrt[3]{25y}}{\sqrt[3]{25y}}$ and simplify if possible: $\dfrac{\sqrt[3]{5y^{2}}}{\sqrt[3]{4x}}=\dfrac{\sqrt[3]{5y^{2}}}{\sqrt[3]{4x}}\cdot\dfrac{\sqrt[3]{25y}}{\sqrt[3]{25y}}=\dfrac{\sqrt[3]{125y^{3}}}{\sqrt[3]{100xy}}=\dfrac{5y}{\sqrt[3]{100xy}}$