Страница 224 номер 812, ГДЗ по алгебре за 9 класс к учебнику Мерзляка
Вычислите: 1) \(\frac{3^{49}}{9^{25}}\); 2) \(\frac{4^8}{8^4}\); 3) \(\frac{5^4 \cdot 11^7}{55^6}\); 4) \(\frac{12^5}{18^3}\).
1)
\(\dfrac{3^{49}}{9^{25}} = 3^{49}:\left( 3^{2} \right)^{25} = 3^{49} \cdot 3^{- 50} = 3^{49 - 50} = 3^{- 1} = \dfrac{1}{3}\)
2)
\(\dfrac{4^{8}}{8^{4}} = \left( 2^{2} \right)^{8}:\left( 2^{3} \right)^{4} = 2^{16}:2^{12} = 2^{16 - 12} = 2^{4} = 16\)
3)
\(\dfrac{5^{4} \cdot 11^{7}}{55^{6}} = \dfrac{5^{4} \cdot 11^{7}}{(5 \cdot 11)^{6}} = \dfrac{5^{4} \cdot 11^{7}}{5^{6} \cdot 11^{6}} = 5^{4 - 6} \cdot 11^{7 - 6} = \dfrac{11}{5^{2}} = \dfrac{11}{25}\)
4)
\(\dfrac{12^{5}}{18^{3}} = \dfrac{3^{5} \cdot 4^{5}}{9^{3} \cdot 2^{3}} = \dfrac{3^{5} \cdot 2^{10}}{3^{6} \cdot 2^{3}} = 3^{5 - 6} \cdot 2^{10 - 3} = \dfrac{2^{7}}{3} = \dfrac{128}{3}\)
Ответ: 1) \(\frac{3^{49}}{9^{25}} = \frac{1}{3}\); 2) \(\frac{4^{8}}{8^{4}} = 16\); 3) \(\frac{5^{4} \cdot 11^{7}}{55^{6}} = \frac{11}{25}\); 4) \(\frac{12^{5}}{18^{3}} = \frac{128}{3}\).
