#### Answer

$\sqrt[3]{\dfrac{9y}{7}}=\dfrac{3y}{\sqrt[3]{21y^{2}}}$

#### Work Step by Step

$\sqrt[3]{\dfrac{9y}{7}}$
Rewrite this expression as $\dfrac{\sqrt[3]{9y}}{\sqrt[3]{7}}$:
$\sqrt[3]{\dfrac{9y}{7}}=\dfrac{\sqrt[3]{9y}}{\sqrt[3]{7}}=...$
Multiply this fraction by $\dfrac{\sqrt[3]{3y^{2}}}{\sqrt[3]{3y^{2}}}$ and simplify if possible:
$...=\dfrac{\sqrt[3]{9y}}{\sqrt[3]{7}}\cdot\dfrac{\sqrt[3]{3y^{2}}}{\sqrt[3]{3y^{2}}}=\dfrac{\sqrt[3]{27y^{3}}}{\sqrt[3]{21y^{2}}}=\dfrac{3y}{\sqrt[3]{21y^{2}}}$