\frac{50^n}{5^{n-1} \cdot 10^{n-2}}

\frac{50^n}{5^{n-1} \cdot 10^{n-2}} = \frac{(2 \cdot 5^2)^n}{5^{n-1} \cdot (2 \cdot 5)^{n-2}} = \frac{2^n \cdot 5^{2n}}{5^{n-1} \cdot 2^{n-2} \cdot 5^{n-2}} = \frac{2^n \cdot 5^{2n}}{2^{n-2} \cdot 5^{2n-3}} = 2^{n-(n-2)} \cdot 5^{2n-(2n-3)} = 2^2 \cdot 5^3 = 4 \cdot 125 = 500