Given the following equation:

$$\frac{n!}{(n-k)!k!}\*\frac{1}{n^{k}}=\frac{1}{k!}\*\frac{n\*(n-1)...(n-k+1)}{n^{k}}$$

(I used \* as the multiplication sign).

I understand $\frac{1}{k!}$ but $$\frac{n\*(n-1)\*...\*(n-k+1)}{n^{k}}$$ is a problem for me. I also understand why $n^{k}$ is in the denominator. I specifically do not understand what happened to $n!$ and $(n-k)!$