  Let $S=\mathbb{K}[x_1,\ldots,x_n]$ the polynomial ring over a field
$\mathbb{K}$. In this paper for some families of monomial ideals $I \subset S$
we study the minimal number of generators of $I^k$. We use this results to find
some other Betti numbers of these families of ideals for special choices of
$n$, the number of variables.
