Hello, I am trying to proof the following claim.

$\displaystyle \left| P(A \times B) \right| = \left| P(B)^A \right|$

Where $\displaystyle P$ is the power set and $\displaystyle P(B)^A := \left \{ \left f: ( f: A \to P(B) \right ) \right \}$.

I am trying to construct a bijection or two injections and cantors theorem to proof they have the same cardinality, but I seem to be getting nowhere. Can anyone help me?