Why can $x^0$ sometimes be simplified to 1 even when x can equal 0?

Question

For example, the Taylor series for $e^x$ is $\sum_{n=0}^{\infty} \frac{x^n}{n!}$. It seems like it should be indeterminate or undefined at $x=0$, since the first term would contain $0^0$, but it's not - the first term is just simplified to $1$.

Edit: answered in Matthew Levy's comment.