There are two ways to solve this problem.
First way:
\({\frac{8}{125}}^{-\frac{2}{3}}\)
\(\sqrt[3]{{(\frac{8}{125})}^{-2}}\)
\(\sqrt[3]{\frac{{8}^{-2}}{{125}^{-2}}}\)
\(\sqrt[3]{\frac{{125}^{2}}{{8}^{2}}}\)
\(\sqrt[3]{\frac{15625}{{8}^{2}}}\)
\(\sqrt[3]{\frac{15625}{64}}\)
\(\frac{\sqrt[3]{15625}}{\sqrt[3]{64}}\)
\(\frac{\sqrt[3]{25\times25\times25}}{\sqrt[3]{64}}\)
\(\frac{25}{\sqrt[3]{64}}\)
\(\frac{25}{\sqrt[3]{4\times4\times4}}\)
\(\frac{25}{4}\)
\(6.25\)
Second way:
\({\frac{8}{125}}^{-\frac{2}{3}}\)
\(\frac{1}{{(\frac{8}{125})}^{\frac{2}{3}}}\)
\(\frac{1}{\frac{{8}^{\frac{2}{3}}}{{125}^{\frac{2}{3}}}}\)
\(\frac{1}{\frac{({2}^{{3})^{\frac{2}{3}}}}{{125}^{\frac{2}{3}}}}\)
\(\frac{1}{\frac{{2}^{\frac{6}{3}}}{{125}^{\frac{2}{3}}}}\)
\(\frac{1}{\frac{{2}^{2}}{{125}^{\frac{2}{3}}}}\)
\(\frac{1}{\frac{4}{{125}^{\frac{2}{3}}}}\)
\(\frac{1}{\frac{4}{({5}^{{3})^{\frac{2}{3}}}}}\)
\(\frac{1}{\frac{4}{{5}^{\frac{6}{3}}}}\)
\(\frac{1}{\frac{4}{{5}^{2}}}\)
\(\frac{1}{\frac{4}{25}}\)
\(1\times\frac{25}{4}\)
\(\frac{25}{4}\)
\(6.25\)
.
