Answer
$\sqrt[3]{x^{2}y^{}}$
Work Step by Step
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\left( \sqrt[6]{x^2y}\right)^2
\\\\=
(x^2y)^{2/6}
.\end{array}
Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(x^2y)^{2/6}
\\\\=
x^{2\cdot\frac{2}{6}}y^{\frac{2}{6}}
\\\\=
x^{\frac{4}{6}}y^{\frac{2}{6}}
\\\\=
x^{\frac{2}{3}}y^{\frac{1}{3}}
.\end{array}
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
x^{\frac{2}{3}}y^{\frac{1}{3}}
\\\\=
\sqrt[3]{x^{2}y^{}}
.\end{array}
