Let $a_i$ be a cardinal number for every $i \in\ I$.
Let $\{A_i\}$ and $\{A'_i\}$ be families of sets and let $A_i$, $A'_i$ and $a_i$ be equipotent for every $i \in I$.
Then show that $\prod_i\ A_i $ is equipotent with $\prod_i\ A'_i $.
This seems obviously true but I don't know how to actually show the bijection between them..