Answer
$\dfrac{6x^2y^3}{\sqrt[]{6z}}$
Work Step by Step
Rationalizing the numerator of $
\sqrt[]{\dfrac{18x^4y^6}{3z}}
$ results to
\begin{array}{l}
\sqrt[]{\dfrac{9x^4y^6\cdot2}{3z}}
\\\\=
3x^2y^3\sqrt[]{\dfrac{2}{3z}}
\\\\=
3x^2y^3\sqrt[]{\dfrac{2}{3z}}
\cdot
\sqrt[]{\dfrac{2}{2}}
\\\\=
3x^2y^3\sqrt[]{\dfrac{4}{6z}}
\\\\=
\dfrac{3x^2y^3\cdot2}{\sqrt[]{6z}}
\\\\=
\dfrac{6x^2y^3}{\sqrt[]{6z}}
.\end{array}