#### Answer

$\dfrac{y\sqrt[4]{45x^3y^2}}{3x}$

#### Work Step by Step

Rationalizing the denominator of the given expression, $
\dfrac{\sqrt[4]{5y^6}}{\sqrt[4]{9x}}
,$ we find:
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[4]{5y^6}}{\sqrt[4]{9x}}\cdot\dfrac{\sqrt[3]{9x^3}}{\sqrt[3]{9x^3}}
\\\\=
\dfrac{\sqrt[4]{45x^3y^6}}{\sqrt[4]{81x^4}}
\\\\=
\dfrac{\sqrt[4]{y^4\cdot45x^3y^2}}{\sqrt[4]{81x^4}}
\\\\=
\dfrac{\sqrt[4]{(y)^4\cdot45x^3y^2}}{\sqrt[4]{(3x)^4}}
\\\\=
\dfrac{y\sqrt[4]{45x^3y^2}}{3x}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.