Страница 41 номер 71, ГДЗ по алгебре за 9 класс к учебнику Алимова с ответами и решением
Вычислить (70—71). 1) \(9^7 : 9^{10}\); 2) \((0{,}2)^2 : (0{,}2)^{-2}\); 3) \(\left(\frac{2}{13}\right)^{-12} : \left(\frac{2}{13}\right)^{-10}\); 4) \(\left(\frac{2}{5}\right)^3 : \left(\frac{2}{5}\right)^{-1}\).
1)
\(\dfrac{9^{7}}{9^{10}} = 9^{7 - 10} = 9^{-3} = \dfrac{1}{9^{3}} = \dfrac{1}{729}\)
2) \((0{,}2)^{2} : (0{,}2)^{-2} = \frac{\left(0{,}2\right)^{2}}{\left(0{,}2\right)^{-2}} = 0{,}2^{2 - (-2)} = 0{,}2^{4} = \left(\frac{1}{5}\right)^{4} = \frac{1}{5^{4}} = \frac{1}{625}\)
3)
\(\left(\dfrac{2}{13}\right)^{-12} : \left(\dfrac{2}{13}\right)^{-10} = \left(\dfrac{2}{13}\right)^{-12 - (-10)} = \left(\dfrac{2}{13}\right)^{-12 + 10} =\)
\(= \left(\dfrac{2}{13}\right)^{-2} = \dfrac{1}{\left(\dfrac{2}{13}\right)^{2}} = \dfrac{1}{\dfrac{2^{2}}{13^{2}}} = \dfrac{13^{2}}{2^{2}} = \dfrac{169}{4} = 42{,}25\)
4)
\(\left(\dfrac{2}{5}\right)^{3} : \left(\dfrac{2}{5}\right)^{-1} = \left(\dfrac{2}{5}\right)^{3 - (-1)} = \left(\dfrac{2}{5}\right)^{3 + 1} = \left(\dfrac{2}{5}\right)^{4} = \dfrac{2^{4}}{5^{4}} = \dfrac{16}{625}\)
