Answer
$\dfrac{x^{\frac{1}{12}}}{y^{\frac{2}{15}}}$
Work Step by Step
RECALL:
(1) $(a^m)^n=a^{mn}$
(2) $(ab)^m = a^mb^m$
(3) $a^{\frac{1}{n}}= \sqrt[n]{a}$
(4) $a^{-m} = \dfrac{1}{a^m}$
Use rule (2) above to obtain:
$=(x^{\frac{1}{4}})^{\frac{1}{3}}(y^{-\frac{2}{5}})^{\frac{1}{3}}$
Use rule (1) above to obtain:
$=x^{\frac{1}{4}\cdot \frac{1}{3}}y^{-\frac{2}{5}(\frac{1}{3})}
\\=x^{\frac{1}{12}}y^{-\frac{2}{15}}$
Use rule (4) above to obtain:
$=x^{\frac{1}{12}} \cdot \dfrac{1}{y^{\frac{2}{15}}}
\\=\dfrac{x^{\frac{1}{12}}}{y^{\frac{2}{15}}}$
