I'm looking for proof of the following commutation relations,
$ [\hat{n}, \hat{a}^k] = -k a^k, \quad \quad \quad \quad [\hat{n}, \hat{a}^{\dagger k}] = -k \hat{a}^{\dagger k} $
where $\hat{n}$ is the number operator $\hat{n} = \hat{a}^{\dagger} \hat{a}$. Does someone have any idea how to prove them? Thanks!!