Pre-Algebra · Superchallenge problem

The number $N = 2^{24}\cdot 3^{36}$ is a perfect square, since $N = (2^{12}\cdot 3^{18})^2$. For how many whole numbers $k \ge 2$ is $N$ a perfect $k$th power, that is, $N = m^{k}$ for some whole number $m$?