Inverting the transformation $u=4xy, v=x^2/y$

Question

I'm trying to invert the transformation $u=4xy, v=x^2/y$. In order to isolate $x$ I did $uv=4x^3$ so $$x=(\frac{uv}{4})^{1/3}$$ and then I substituted this expression into $u=4xy$ to obtain $$y=\frac{u}{4x}=\frac{u^{2/3}}{v^{1/3}4^{2/3}}$$. However, I'm not sure if this is the simplest way I can expression $x,y$ in terms of $u,v$.

Answer 1

Hint: cube $y$, then take the cube root again. It'll look neater that way.