Answer
$\dfrac{y^{1/10}}{x^{1/12}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( x^{-1/3}y^{2/5} \right)^{1/4}
,$ simplifies to
\begin{array}{l}\require{cancel}
x^{\left( -\frac{1}{3} \right) \left( \frac{1}{4} \right)}y^{\left( \frac{2}{5} \right) \left( \frac{1}{4} \right)}
\\\\=
x^{-\frac{1}{12}}y^{\frac{2}{20}}
\\\\=
x^{-\frac{1}{12}}y^{\frac{1}{10}}
\\\\=
\dfrac{y^{\frac{1}{10}}}{x^{\frac{1}{12}}}
\\\\=
\dfrac{y^{1/10}}{x^{1/12}}
.\end{array}
