My textbook (Naive Set Theory) asks the reader to show that $\left| E^F \right|$ = $\left| E \right| ^ \left| F \right|$ for all finite sets. In passing to induction, I noticed that this would imply that $0^0 = 1$, since there exists the trivial empty function (i.e., $\emptyset \times \emptyset = \emptyset$). The definition of exponentiation in $\omega$ says that $(\forall m \in \omega $ $(m^0 = 1))$, so this seems reasonable.
Is this correct, or should this case be discarded? If it is correct, is it correct in $\omega$ only, or everywhere?