Сократите дробь (8*100^n)/(2^(2n+1)*5^(2n-2)).

\[\frac{8 \cdot 100^{n}}{2^{2n + 1} \cdot 5^{2n - 2}} = \frac{2^{3} \cdot 5^{2n} \cdot 2^{2n}}{2^{2n} \cdot 2 \cdot \frac{5^{2n}}{5^{2}}} = \frac{2^{2}}{\frac{1}{5^{2}}} =\]

\[= 4 \cdot 25 = 100.\]