Answer
$\frac{x y}{z} \sin \left(\pi x^{3} y z^{4}\right)=g(u(x, y, z), v(x, y, z), w(x, y, z))$
Work Step by Step
Given:
\[
z \sin x y=g(x, y, z)
\]
$u(x, y, z)=\pi x y z$ and $w(x, y, z)=x^{2} z^{3}, v(x, y, z)=\frac{x y}{z}$
We have to calculate $g(u(x, y, z), v(x, y, z), w(x, y, z)),$ substituting $x, y$ and $z$ in the function:
\[
\begin{aligned}
z \sin x y=g(x, y, z) & \\
w(x, y, z) \sin u(x, y, z) * v(x, y, z)=g(u(x, y, z), v(x, y, z), w(x, y, z)) & \\
\frac{x y}{z} \sin \left(x^{2} z^{3} * \pi x y z\right)=g(u(x, y, z), v(x, y, z), w(x, y, z)) & \\
\frac{x y}{z} \sin \left(\pi x^{3} y z^{4}\right) =g(u(x, y, z), v(x, y, z), w(x, y, z)) &
\end{aligned}
\]
