Simplify the Radical Expression (xy^2)^(1/3)

${(x y^{2})}^{\frac{1}{3}}$

Apply the product rule to $x y^{2}$ .

$x^{\frac{1}{3}} {(y^{2})}^{\frac{1}{3}}$

Multiply the exponents in ${(y^{2})}^{\frac{1}{3}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{3}} y^{2 (\frac{1}{3})}$

Combine $2$ and $\frac{1}{3}$ .

$x^{\frac{1}{3}} y^{\frac{2}{3}}$