Answer
$\sqrt[20]{x}$
Work Step by Step
RECALL:
(1) $\sqrt[n]{a} = a^{\frac{1}{n}}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
Use rule (1) above to obtain:
$=\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{5}}}$
Use rule (2) above to obtain:
$=x^{\frac{1}{4}-\frac{1}{5}}$
Make the fractions similar using their LCD of $20$ to obtain:
$=x^{\frac{5}{20} - \frac{4}{20}}
\\=x^{\frac{5-4}{20}}
\\=x^{\frac{1}{20}}$
Use rule (1) above to obtain:
$=\sqrt[20]{x}$
