Mellin Transform of Higher Order Exponential

Theorem
Let $a$ be a complex constant.

Let $n$ be a natural number.

Let $e^t$ be the complex exponential.

Let $\mathcal M$ be the Mellin transform.

Then:
 * $\mathcal M \left\{ {e^{-a t^n} }\right\} \left({s}\right) = \dfrac {a^{-s/n} } n \Gamma \left({\dfrac s n}\right)$

where $\Gamma \left({z}\right)$ is the Gamma function and $\Re \left({a}\right)$, $\Re \left({s}\right) > 0$.