Write a matrix in terms of a other matrix

Question

Let $M:=(m_{ij})_{i,j=1,...,n}$ be a matrix. If there is a matrix $N:=(m_{ij}^l)_{i,j=1,...,n}$, $l\in\mathbb{N}$, is there any option to write $N$ in terms of $M$? Something like $N=M^{l}$?