#### Answer

$\dfrac{x^4}{\sqrt[3]{2}\sqrt[7]{y^2}}$

#### Work Step by Step

Using the laws of exponents, the given expression, $
2^{-1/3}x^4y^{-2/7}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{x^4}{2^{1/3}y^{2/7}}
.\end{array}
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $
\dfrac{x^4}{2^{1/3}y^{2/7}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^4}{\sqrt[3]{2^1}\sqrt[7]{y^2}}
\\\\=
\dfrac{x^4}{\sqrt[3]{2}\sqrt[7]{y^2}}
.\end{array}