Answer
$\dfrac{m^{1/3}}{n^{1/8}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( m^{2/3}n^{-1/4} \right)^{1/2}
,$ simplifies to
\begin{array}{l}\require{cancel}
m^{\left( \frac{2}{3} \right) \left( \frac{1}{2} \right)}n^{\left( -\frac{1}{4} \right) \left( \frac{1}{2} \right)}
\\\\=
m^{\frac{2}{6}}n^{-\frac{1}{8}}
\\\\=
\dfrac{m^{\frac{1}{3}}}{n^{\frac{1}{8}}}
\\\\=
\dfrac{m^{1/3}}{n^{1/8}}
.\end{array}
