Particles are subject to collisions that cause them to split into two parts with each part a

Question:

Particles are subject to collisions that cause them to split into two parts with each part a fraction of the parent. Suppose that this fraction is uniformly distributed between 0 and 1. Following a single particle through several splittings we obtain a fraction of the original particle Zn = X1 ·X2 · . . . ·Xn where each Xj is uniformly distributed between 0 and 1. Show that the density for the random variable Zn is