I need to prove that the set $\{A^n : n \in \mathbb{N} \}$ using the ZFC axioms (without Replacement).
My (rough) plan would be to construct some set containing "more" sets than necessary, then use the comprehension axiom to remove the undesirable sets. Something like: for some $Y$, $\{ X \in Y : \exists n \in \mathbb{N}, X = A^n\}$.
I know how to prove that any one of these sets (e.g., $A^2$), exists, but I have no idea how to prove that the set containing all of these powers exists.