  For fixed $m>1$, we consider $m$ independent $n \times n$ non-Hermitian
random matrices $X_1, ..., X_m$ with i.i.d. centered entries with a finite
$(2+\eta)$-th moment, $ \eta>0.$ As $n$ tends to infinity, we show that the
empirical spectral distribution of $n^{-m/2} \*X_1 X_2 ... X_m$ converges, with
probability 1, to a non-random, rotationally invariant distribution with
compact support in the complex plane. The limiting distribution is the $m$-th
power of the circular law.
