$\frac{ \sqrt[3]{8{x}^{2}} }{ \sqrt[3]{y} }$
Simplify the radical expression$\frac{ 2\sqrt[3]{{x}^{2}} }{ \sqrt[3]{y} }$
Multiply the fraction by $\frac{ \sqrt[3]{{y}^{2}} }{ \sqrt[3]{{y}^{2}} }$$\frac{ 2\sqrt[3]{{x}^{2}} }{ \sqrt[3]{y} } \times \frac{ \sqrt[3]{{y}^{2}} }{ \sqrt[3]{{y}^{2}} }$
To multiply the fractions, multiply the numerators and denominators separately$\frac{ 2\sqrt[3]{{x}^{2}}\sqrt[3]{{y}^{2}} }{ \sqrt[3]{y}\sqrt[3]{{y}^{2}} }$
Calculate the product$\frac{ 2\sqrt[3]{{x}^{2}{y}^{2}} }{ \sqrt[3]{y}\sqrt[3]{{y}^{2}} }$
The product of roots with the same index is equal to the root of the product$\frac{ 2\sqrt[3]{{x}^{2}{y}^{2}} }{ \sqrt[3]{y \times {y}^{2}} }$
Calculate the product$\frac{ 2\sqrt[3]{{x}^{2}{y}^{2}} }{ \sqrt[3]{{y}^{3}} }$
Reduce the index of the radical and exponent with $3$$\frac{ 2\sqrt[3]{{x}^{2}{y}^{2}} }{ y }$