ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 1263

\[\boxed{\text{1263.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[\textbf{а)}\ \frac{2^{m} \cdot 3^{n - 1} - 2^{m - 1} \cdot 3^{n}}{2^{m} \cdot 3^{n}} =\]

\[= \frac{2^{m} \cdot \frac{3^{n}}{3} - \frac{2^{m}}{2} \cdot 3^{n}}{2^{m} \cdot 3^{n}} =\]

\[= \frac{\frac{2^{m}3^{n}}{3} - \frac{2^{m}3^{n}}{2}}{2^{m} \cdot 3^{n}} =\]

\[= \frac{2 \cdot 2^{m} \cdot 3^{n} - 2^{m} \cdot 3 \cdot 3^{n}}{\frac{6}{2^{m} \cdot 3^{n}}} =\]

\[= \frac{2^{m} \cdot 3^{n}(2 - 3)}{6 \cdot 2^{m} \cdot 3^{n}} = \frac{2 - 3}{6} = - \frac{1}{6}\]

\[\textbf{б)}\ \frac{5^{n + 1} \cdot 2^{n - 2} + 5^{n - 2} \cdot 2^{n - 1}}{10^{n - 2}} =\]

\[= \frac{5^{n} \cdot 5 \cdot \frac{2^{n}}{2^{2}} + \frac{5^{n}}{5^{2}} \cdot \frac{2^{n}}{2}}{\frac{10^{n}}{10^{2}}} =\]

\[= \frac{5^{3} \cdot 5^{n} \cdot 2^{n} + 2 \cdot 2^{n} \cdot 5^{n}}{5^{2} \cdot 2^{2}} \cdot\]

\[\cdot \frac{10^{2}}{10^{n}} = \frac{2^{n} \cdot 5^{n}\left( 5^{3} + 2 \right)}{10^{n}} =\]

\[= 125 + 2 = 127\]

\[\textbf{в)}\ \frac{5^{m} \cdot 4^{n}}{5^{m - 2} \cdot 2^{2n} + 5^{m} \cdot 2^{2n - 1}} =\]

\[= \frac{5^{m} \cdot 4^{n}}{\frac{5^{m}}{5^{2}} \cdot 2^{2n} + 5^{m} \cdot \frac{2^{2n}}{2}} =\]

\[= \frac{5^{m} \cdot 4^{n}}{\frac{5^{m} \cdot 2^{2n} \cdot 2 + 5^{2} \cdot 5^{m} \cdot 2^{2n}}{2 \cdot 5^{2}}} =\]

\[= \frac{5^{m} \cdot 4^{n} \cdot 2 \cdot 5^{2}}{2^{2n} \cdot 5^{m} \cdot \left( 2 + 5^{2} \right)} = \frac{50}{27} =\]

\[= 1\frac{23}{27}\]

\[\textbf{г)}\ \frac{21^{n}}{3^{n - 1}7^{n + 1} + 3^{n}7^{n}} =\]

\[= \frac{3^{n} \cdot 7^{n}}{\frac{3^{n}}{3} \cdot 7^{n} \cdot 7 + 3^{n}7^{n}} =\]

\[= \frac{3^{n} \cdot 7^{n}}{\frac{3^{n} \cdot 7^{n} \cdot 7 + 3^{n} \cdot 7^{n} \cdot 3}{3}} =\]

\[= \frac{3 \cdot 3^{n} \cdot 7^{n}}{3^{n} \cdot 7^{n}(7 + 3)} = \frac{3}{10} = 0,3\]