In how many ways can I extend the basis of a vector space over a finite field?

Question

Suppose I've a finite field, say for convenience $\mathbb F_p$, and I take the two extensions $\mathbb F^{p^m}$ and $\mathbb F^{p^n}$ as vector spaces over it. If $m<n$ and $m|n$, in how many ways can I get a basis for $\mathbb F^{p^n}$ from a basis of $\mathbb F^{p^m}$? Is there any way to count this easily?