Answer
$\sqrt[12]{x}$
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:
$=\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{4}}}$
Use rule (2) above to obtain:
$=x^{\frac{1}{3}-\frac{1}{4}}$
Make the fractions similar using their LCD of $12$ to obtain:
$=x^{\frac{4}{12} - \frac{3}{12}}
\\=x^{\frac{4-3}{12}}
\\=x^{\frac{1}{12}}$
Use rule (1) above to obtain:
$=\sqrt[12]{x}$
