Inverse Laplace transform with an arbitrary parameter

Question

I am trying to find this: \begin{equation} \mathcal{L}^{-1}(s^nF(s))=?, \end{equation} where the parameter $n$ can be an arbitrary value. I know when $n$ is a positive integer, it can be written as a differentiated form; while when $n$ is a negative integer, it can be written as a integrated for. But can a general form be presented? Thanks!