How to define complex powers of $0$?

I'm studying Complex Analysis, and I've seen the definition of the set-valued power function as follows

Let $z,w \in \mathbb{C}$, then $z^{w} \equiv \exp(w\log z)$.

If I recall correctly. Now it seems there is something wrong with this definition, because you can't use it to define powers of $0$, which should naturally be $0$. Am I missing something? Or is the definition 'weird'?