\[\boxed{\mathbf{845\ (845).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \frac{100^{n}}{2^{2n + 3} \cdot 5^{2n + 1}} =\]
\[= \frac{10^{2n}}{2^{2n} \cdot 2³ \cdot 5^{2n} \cdot 5} = \frac{1}{40}\]
\[2)\ \frac{2^{2n + 1} \cdot 7^{n + 1}}{6 \cdot 28^{n}} =\]
\[= \frac{2^{2n} \cdot 2 \cdot 7^{n} \cdot 7}{2^{2n} \cdot 7^{n} \cdot 6} = \frac{7}{3}\]
\[3)\ \frac{5^{n + 1} - 5^{n}}{2 \cdot 5^{n}} = \frac{5^{n}(5 - 1)}{2 \cdot 5^{n}} =\]
\[= \frac{4}{2} = 2\]
\[4)\ \frac{18^{n}}{3^{2n + 2} \cdot 2^{n + 3}} =\]
\[= \frac{3^{2n} \cdot 2^{n}}{3^{2n} \cdot {9 \cdot 2}^{n} \cdot 8} = \frac{1}{72}\]
\[5)\ \frac{41 \cdot 9^{n}}{9^{n + 2} + 9^{n}} = \frac{41 \cdot 9^{n}}{9^{n}(81 + 1)} =\]
\[= \frac{41}{82} = \frac{1}{2}\]