$ϕ(m · n) = \frac{ϕ(m) · ϕ(n) · gcd(m, n)}{ϕ(gcd(m, n))}$

Deduce from the previous identity that $ϕ(n^k) = n^{k−1}· ϕ(n)$

I know that \begin{eqnarray*} \phi(m) = m \prod_{p \mid m } (1-\frac{1}{p}). \\ \end{eqnarray*}

How can I make use of that? Any help please?