  We study the number of generators of ideals in regular rings and ask the
question whether $\mu(I)<\mu(I^2)$ if $I$ is not a principal ideal, where
$\mu(J)$ denotes the number of generators of an ideal $J$. We provide lower
bounds for the number of generators for the powers of an ideal and also show
that the CM-type of $I^2$ is $\geq 3$ if $I$ is a monomial ideal of height $n$
in $K[x_1,\ldots,x_n]$ and $n\geq 3$.
