Answer
$\sqrt[10]{a^{3}y^{7}}$
Work Step by Step
$\sqrt[5]{a^{4}y^{6}} = (a^{4}y^{6})^{1/5}=a^{4/5}\cdot y^{6/5}$
$\sqrt{ay}= a^{1/2}y^{1/2}$
$\displaystyle \frac{\sqrt[5]{a^{4}y^{6}}}{\sqrt{ay}}=\frac{a^{4/5}\cdot y^{6/5}}{a^{1/2}y^{1/2}}\qquad$... apply $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
$=a^{4/5-1/2}\cdot y^{6/5-1/2}$
$=a^{\frac{8-5}{10}}y^{\frac{12-5}{10}}$
$=a^{3/10}y^{7/10}$
$=(a^{3}y^{7})^{1/10}$
$=\sqrt[10]{a^{3}y^{7}}$
