How to prove that $87!<16! \left(52^{71}\right)$ Prove that
$$87!<16! \left(52^{71}\right)$$
I do not how can i compare between the factorials or what the procedure to solve such questions?

AM-GM gives:
$$\frac1{71}\sum_{i=1}^{71}(i+16)>\sqrt[71]{\prod_{i=1}^{71}(i+16)}$$
So:
$$\frac1{71}\left(\frac{71(71+1)}{2}+71\cdot 16\right)>\sqrt[71]{\frac{87!}{16!}}$$
or:
$$52^{71}>\frac{87!}{16!}\implies 16!(52^{71})>87!$$
