Answer
$\sqrt[20]{a}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}$ and the laws of exponents, then,
\begin{array}{l}
\dfrac{\sqrt[4]{a}}{\sqrt[5]{a}}
\\\\=
\dfrac{a^{1/4}}{a^{1/5}}
\\\\=
a^{\frac{1}{4}-\frac{1}{5}}
\\\\=
a^{\frac{5}{20}-\frac{4}{20}}
\\\\=
a^{\frac{1}{20}}
\\\\=
\sqrt[20]{a^1}
\\\\=
\sqrt[20]{a}
.\end{array}
