elementary set theory - Prove that $ ^{mathbb{N}}mathcal P left({mathbb{N}}right) sim mathcal P left({mathbb{N}}right) $

The set of all functions from $ A $ to $ B $ is denoted $ ^{A}B $. Prove that $ ^{\mathbb{N}}\mathcal P \left({\mathbb{N}}\right) \sim \mathcal P \left({\mathbb{N}}\right) $.

Previous question proved that for any set $ A $, $ ^{A}\{yes,no\}\sim \mathcal P \left({A}\right) $. The symbol $ \sim $ means equinumerous to. $\mathbb{N}$ does not include $0$ here. $\mathcal P$ is power set operation. I know we have to create a bijection between $ ^{\mathbb{N}}\mathcal P \left({\mathbb{N}}\right) \sim \mathcal P \left({\mathbb{N}}\right) $. I believe I might be close to a solution, but am looking for some suggestions first.