Страница 40 номер 66, ГДЗ по алгебре за 9 класс к учебнику Алимова с ответами и решением
Вычислить (66—67). 1) \(\left(\frac{10}{3}\right)^{-3}\); 2) \(\left(-\frac{9}{11}\right)^{-2}\); 3) \((0{,}2)^{-4}\); 4) \((0{,}5)^{-5}\); 5) \(-(-17)^{-1}\); 6) \(-(-13)^{-2}\).
1)
\(\left(\dfrac{10}{3}\right)^{-3} = \dfrac{1}{\left(\dfrac{10}{3}\right)^{3}} = \dfrac{1}{\dfrac{10^{3}}{3^{3}}} = \dfrac{3^{3}}{10^{3}} = \dfrac{27}{1000} = 0{,}027\)
2)
\(\left(-\dfrac{9}{11}\right)^{-2} = \dfrac{1}{\left(-\dfrac{9}{11}\right)^{2}} = \dfrac{1}{\dfrac{\left(-9\right)^{2}}{11^{2}}} = \dfrac{11^{2}}{\left(-9\right)^{2}} = \dfrac{121}{81} = 1\dfrac{40}{81}\)
3) \((0{,}2)^{-4} = \left(\frac{1}{5}\right)^{-4} = \frac{1}{\left(\frac{1}{5}\right)^{4}} = \frac{5^{4}}{1} = 625\)
4) \((0{,}5)^{-5} = \left(\frac{1}{2}\right)^{-5} = \frac{1}{\left(\frac{1}{2}\right)^{5}} = \frac{1}{\frac{1}{2^{5}}} = 2^{5} = 32\)
5) \(-(-17)^{-1} = -\frac{1}{\left(-17\right)^{1}} = -\left(-\frac{1}{17}\right) = \frac{1}{17}\)
6) \(-(-13)^{-2} = -\frac{1}{\left(-13\right)^{2}} = -\frac{1}{13^{2}} = -\frac{1}{169}\)
