Answer
$\dfrac{\sqrt[4]{250}}{5}$
Work Step by Step
Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index, the given expression, $
\dfrac{\sqrt[4]{2}}{\sqrt[4]{5}}
,$ is equivalent to
\begin{align*}
&
=\dfrac{\sqrt[4]{2}}{\sqrt[4]{5}}\cdot\dfrac{\sqrt[4]{5^3}}{\sqrt[4]{5^3}}
\\\\&=
\dfrac{\sqrt[4]{2(5^3)}}{\sqrt[4]{5^4}}
\\\\&=
\dfrac{\sqrt[4]{250}}{5}
.\end{align*}
Hence, the simplified form of the given expression is $
\dfrac{\sqrt[4]{250}}{5}
$.
