Proposition 11

Let $\mathfrak{a}$ be a cardinal. Then $\mathfrak{a}^0 = 1$, $\mathfrak{a}^1 = \mathfrak{a}$, $1^{\mathfrak{a}} = 1$; and $0^{\mathfrak{a}} = 0$ if $\mathfrak{a} \neq 0$.

For there exists a unique mapping of $\varnothing$ into any given set (namely, the mapping whose graph is the empty set); the set of mappings of a set consisting of a single element into an arbitrary set X is equipotent to X (Chapter II, § 5, no. 3); there exists a unique mapping of an arbitrary set into a set consisting of a single element; and, finally, there is no mapping of a non-empty set into $\varnothing$.

¶ Note in particular that $0^0 = 1$.