Найдите значение выражения
\(\displaystyle \left(\frac{1}{8}\right)^{-\frac{2}{3}}+(0{,}0016)^{-0{,}{25}}\small.\)
Сначала найдем \(\displaystyle \left(\frac{1}{8}\right)^{-\frac{2}{3}}\small,\) затем \(\displaystyle (0{,}0016)^{-0{,}{25}}\small, \) потом найдем сумму.
Получаем
\(\displaystyle \left(\frac{1}{8}\right)^{-\frac{2}{3}}=\left(\frac{1}{8}\right)^{\frac{\color{blue}{-2}}{\color{red}{3}}}=\sqrt[{\color{red}{3}}]{\left(\frac{1}{8}\right)^\color{blue}{-2}}=\sqrt[3]{{8^2}}=\sqrt[3]{{64}}=4\small,\)
\(\displaystyle (0{,}0016)^{-0{,}{25}}=(0{,}0016)^{-\frac{1}{4}}=(0{,}0016)^{\frac{\color{blue}{-1}}{\color{red}{4}}}=\sqrt[{\color{red}{4}}]{(0{,}0016)^\color{blue}{-1}}=\sqrt[4]{\frac{1}{0{,}0016}}=\sqrt[4]{625}=5\small,\)
\(\displaystyle \left(\frac{1}{8}\right)^{-\frac{2}{3}}+(0{,}0016)^{-0{,}{25}}=4+5=9\small.\)
Ответ: \(\displaystyle 9\small.\)