Answer
$\dfrac{y}{z^{1/6}}$
Work Step by Step
Using laws of exponents, then,
\begin{array}{l}
\dfrac{(y^3z)^{1/6}}{y^{-1/2}z^{1/3}}
\\\\=
\dfrac{y^{3\cdot\frac{1}{6}}z^{\frac{1}{6}}}{y^{\frac{-1}{2}}z^{\frac{1}{3}}}
\\\\=
\dfrac{y^{\frac{3}{6}}z^{\frac{1}{6}}}{y^{\frac{-1}{2}}z^{\frac{1}{3}}}
\\\\=
y^{\frac{3}{6}-\frac{-1}{2}}z^{\frac{1}{6}-\frac{1}{3}}
\\\\=
y^{\frac{3}{6}+\frac{3}{6}}z^{\frac{1}{6}-\frac{2}{6}}
\\\\=
y^{\frac{6}{6}}z^{-\frac{1}{6}}
\\\\=
\dfrac{y}{z^{1/6}}
.\end{array}
