#### Answer

$\dfrac{5x\sqrt{2x}}{9y^4}$

#### Work Step by Step

RECALL:
The quotient rule:
$\sqrt[n]{\dfrac{a}{b}}=\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$
where
$\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$
Use the quotient rule above to obtain:
$=\dfrac{\sqrt{50x^3}}{\sqrt{81y^{8}}}
\\=\dfrac{\sqrt{25x^2(2x)}}{\sqrt{(9y^4)^2}}
\\=\dfrac{\sqrt{(5x)^2(2x)}}{9y^4}
\\=\dfrac{5x\sqrt{2x}}{9y^4}$