Answer
$x=\displaystyle \frac{kz^{1/3}}{y}$
$y=\displaystyle \frac{kz^{1/3}}{x}$
Work Step by Step
(cube root of z =$ \sqrt[3]{z}=z^{1/3})$
$x$ varies directly as $z^{1/3}:\qquad x=kz^{1/3}$
$x$ varies inversely as $y :\displaystyle \qquad x=\frac{k}{y}$
Combined (jointly): $\displaystyle \qquad x=\frac{kz^{1/3}}{y}$
Solving for $y,$
multiplpy both sides by y (get it out of the denominator)
$xy=kz^{1/3}\qquad/\div x$
$y=\displaystyle \frac{kz^{1/3}}{x}$
