11) $\left(\left(\frac{125}{8}\right)^{\frac{2}{3}}\right)^{-\frac{1}{2}}$

Question

$Фото задания: 11) $\left(\left(\frac{125}{8}\right)^{\frac{2}{3}}\right)^{-\frac{1}{2}}$$ Фото задания

Accepted Answer

\[\left(\frac{125}{8}\right)^{\frac{2}{3}}=\left(\sqrt[3]{\frac{125}{8}}\right)^2=\left(\frac{5}{2}\right)^2=\frac{25}{4}.\]

\[\left(\frac{25}{4}\right)^{-\frac{1}{2}}=\left(\frac{4}{25}\right)^{\frac{1}{2}}=\frac{2}{5}.\]

Ответ: $\frac{2}{5}$

11) \(\left(\left(\frac{125}{8}\right)^{\frac{2}{3}}\right)^{-\frac{1}{2}}\)