Mellin Transform of Power Times Function

Theorem
Let $t^n: \R \to \R$ be $t$ to the $n$th power for some $n \in \N_{\ge 0}$.

Let $\mathcal M$ be the Mellin transform.

Then:
 * $\mathcal M \left\{ {t^n f \left({t}\right)} \right\} \left({s}\right) = \mathcal M \left\{ {f \left({t}\right)}\right\} \left({s + n}\right)$

for both transforms exist.