#### Answer

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

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt[4]{\dfrac{x^9y^{12}}{z^{6}}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[4]{x^9y^{12}}}{\sqrt[4]{z^{6}}}
\\\\=
\dfrac{\sqrt[4]{x^8y^{12}\cdot x}}{\sqrt[4]{z^{4}\cdot z^2}}
\\\\=
\dfrac{\sqrt[4]{(x^2y^{3})^4\cdot x}}{\sqrt[4]{(z)^{4}\cdot z^2}}
\\\\=
\dfrac{x^2y^{3}\sqrt[4]{x}}{z\sqrt[4]{z^2}}
\\\\=
\dfrac{x^2y^{3}}{z}\sqrt[4]{\dfrac{x}{z^2}}
\end{array}
* Note that it is assumed that all variables represent positive numbers.