Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set - Page 717: 10

$\dfrac{5}{\sqrt[3]{3y}}=\dfrac{5\sqrt[3]{9y^{2}}}{3y}$

$\dfrac{5}{\sqrt[3]{3y}}$ Multiply the fraction by $\dfrac{\sqrt[3]{9y^{2}}}{\sqrt[3]{9y^{2}}}$ and simplify: $\dfrac{5}{\sqrt[3]{3y}}=\dfrac{5}{\sqrt[3]{3y}}\cdot\dfrac{\sqrt[3]{9y^{2}}}{\sqrt[3]{9y^{2}}}=\dfrac{5\sqrt[3]{9y^{2}}}{\sqrt[3]{27y^{3}}}=\dfrac{5\sqrt[3]{9y^{2}}}{3y}$