Suppose that $X$ has the exponential distribution. Find the density for $X^3$ 
Suppose that $X$ has the exponential distribution. Find the density for $X^3$.

Really not sure where to go with this problem, my notes from class weren't sufficient and after poking around online couldn't find anything to get me going. Any hints/help are really appreciated.

As is the case here the transformation $z = g(x) = x^3$ is one-to-one over the support and has the inverse transformation
$$x = g^{-1}(z) = h(z) = \sqrt[3]{z}$$
then the pdf of $Z$ is given by
$$f_Z(z) = f_X(x)\left|\frac{dx}{dz}\right| = f_X[h(z)]\left|\frac{dh(z)}{dz}\right| = f_X[\sqrt[3]{z}]\left|\frac{d\sqrt[3]{z}}{dz}\right| $$
