  We derive a formula for the moments and the free cumulants of the
multiplication of $k$ free random variables in terms of $k$-equal and
$k$-divisible non-crossing partitions. This leads to a new simple proof for the
bounds of the right-edge of the support of the free multiplicative convolution
$\mu^{\boxtimes k}$, given by Kargin which show that the support grows at most
linearly with $k$. Moreover, this combinatorial approach generalize the results
of Kargin since we do not require the convolved measures to be identical. We
also give further applications, such as a new proof of the limit theorem of
Sakuma and Yoshida.
