I have such function $f: \mathbb{N} \to 2^\mathbb{N}$, $(0\in \mathbb{N})$; $f(n) = \{ k\in \mathbb{N} :2^k | n\}$. Find image of $f(P)$ and $f^{-1}(P)$, where $P$ is a set of prime numbers.

I actually dont understand what $2^\mathbb{N}$ is, is it a set of all subsets of $\mathbb{N}$?