Answer
$\dfrac{\sqrt[4]{xy^3}}{3y^2}$
Work Step by Step
Rationalizing the denominator or $
\dfrac{\sqrt[4]{x}}{\sqrt[4]{81y^5}}
$ simplifies to
\begin{array}{l}
\dfrac{\sqrt[4]{x}}{\sqrt[4]{3^4y^4\cdot y}}
\\\\=
\dfrac{\sqrt[4]{x}}{3|y|\sqrt[4]{y}}
\\\\=
\dfrac{\sqrt[4]{x}}{3|y|\sqrt[4]{y}}\cdot\dfrac{\sqrt[4]{y^3}}{\sqrt[4]{y^3}}
\\\\=
\dfrac{\sqrt[4]{xy^3}}{3|y|\sqrt[4]{y^4}}
\\\\=
\dfrac{\sqrt[4]{xy^3}}{3|y|\cdot|y|}
\\\\=
\dfrac{\sqrt[4]{xy^3}}{3y^2}
.\end{array}
