\frac{100^n}{5^{2n-1} \cdot 4^{n-2}}

\frac{100^n}{5^{2n-1} \cdot 4^{n-2}} = \frac{(2^2 \cdot 5^2)^n}{5^{2n-1} \cdot (2^2)^{n-2}} = \frac{2^{2n} \cdot 5^{2n}}{5^{2n-1} \cdot 2^{2n-4}} = 2^{2n-(2n-4)} \cdot 5^{2n-(2n-1)} = 2^4 \cdot 5^1 = 16 \cdot 5 = 80