Answer
$\dfrac{x^{\frac{1}{4}}}{y^{\frac{3}{10}}}$
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:
$=(x^{\frac{1}{2}})^{\frac{1}{2}}(y^{-\frac{3}{5}})^{\frac{1}{2}}$
Use rule (1) above to obtain:
$=x^{\frac{1}{2}\cdot \frac{1}{2}}y^{-\frac{3}{5}(\frac{1}{2})}
\\=x^{\frac{1}{4}}y^{-\frac{3}{10}}$
Use rule (4) above to obtain:
$=x^{\frac{1}{4}} \cdot \dfrac{1}{y^{\frac{3}{10}}}
\\=\dfrac{x^{\frac{1}{4}}}{y^{\frac{3}{10}}}$
