jmc

For every divisor $d$ of $50$, then $50/d$ is also a divisor of $50$. Their product is $d\cdot (50/d)=50$. It follows that every divisor can be paired with another divisor of $50$ such that their product is $50=2\cdot 5^2$. There are $(1+1)(2+1)=6$ divisors of $50$: $1,2,5,10,25,50$. Thus, the answer is $50^{6/2}=50^3=\boxed{125,000}$.