Решебник по алгебре 9 класс Мерзляк Задание 812

\[\boxed{\mathbf{812\ (812).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{3^{49}}{9^{25}} = \frac{3^{49}}{\left( 3^{2} \right)^{25}} = \frac{3^{49}}{3^{50}} = \frac{1}{3}\]

\[2)\ \frac{4^{8}}{8^{4}} = \frac{\left( 2^{2} \right)^{8}}{\left( 2^{3} \right)^{4}} = \frac{2^{16}}{2^{12}} = 2^{4} = 16\]

\[3)\ \frac{5^{4} \cdot 11^{7}}{55^{6}} = \frac{5^{4} \cdot 11^{7}}{5^{6} \cdot 11^{6}} = \frac{11}{5^{2}} = \frac{11}{25}\]

\[4)\ \frac{12^{5}}{18^{3}} = \frac{4^{5} \cdot 3^{5}}{9^{3} \cdot 2^{3}} = \frac{\left( 2^{2} \right)^{5} \cdot 3^{5}}{\left( 3^{2} \right)^{3} \cdot 2^{3}} =\]

\[= \frac{2^{10} \cdot 3^{5}}{3^{6} \cdot 2³} = \frac{2^{7}}{3} = \frac{128}{3}\ \]