Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 1 / e / i / Solution

Each of the $m$ elements of $A$ independently receives one of $n$ images in $B$. The multiplication principle therefore gives $n^m$ functions. In particular an empty set domain has exactly one function to any $B$, so here $0^0$ is interpreted as $1$; a nonempty domain has no function to an empty set codomain.