Решебник по алгебре 8 класс Мерзляк Задание 880

\[\boxed{\mathbf{880\ (880).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{9^{n - 1}}{3^{2n - 3}} = \frac{\left( 3^{2} \right)^{n - 1}}{3^{2n - 3}} = \frac{3^{2n - 2}}{3^{2n - 3}} = 3\]

\[2)\ \frac{7^{n + 1} \cdot 2^{n - 1}}{14^{n}} =\]

\[= \frac{7^{n} \cdot 7 \cdot 2^{n} \cdot 2^{- 1}}{7^{n} \cdot 2^{n}} = \frac{7}{2} = 3,5\]

\[3)\ \frac{2^{2n - 1} \cdot 3^{n + 1}}{12^{n}} =\]

\[= \frac{2^{2n} \cdot 2^{- 1} \cdot 3^{n} \cdot 3}{2^{2n} \cdot 3^{n}} = \frac{3}{2} = 1,5\]

\[4)\ \frac{a^{6} + a^{11}}{a^{- 4} + a} = \frac{a^{6}(1 + a^{5})}{a^{- 4}(1 + a^{5})} = a^{10}\]

\[5)\ \frac{a^{- 3} + a^{- 2} + a^{- 1}}{a^{3} + a^{2} + a} =\]

\[= \frac{a^{- 3}(1 + a + a^{2})}{a(a^{2} + a + 1)} = \frac{1}{a^{4}}\]

\[6)\ \frac{6^{n + 2} - 6^{n}}{35} = \frac{6^{n}(36 - 1)}{35} = 6^{n}\]

\[7)\ \frac{5^{n + 2} - 5^{n - 2}}{5^{n}} =\]

\[= \frac{5^{n}\left( 5^{2} - 5^{- 2} \right)}{5^{n}} = 25 - \frac{1}{25} =\]

\[= 24\frac{24}{25}\]

\[8)\ \frac{2^{- n} + 1}{2^{n} + 1} = \frac{2^{- n}(1 + 2^{n})}{(2^{n} + 1)} = \frac{1}{2^{n}}\]