# Simplify 64 / 125 raised to the power -⅔.

The given expression is

$$\left(\frac{64}{125}\right)^{-\frac{2}{3}} =\left(\frac{64}{125}\right)^{(-1) \frac{2}{3}} =\left(\left(\frac{64}{125}\right)^{-1}\right)^{\frac{2}{3}} =\left(\frac{1}{\frac{64}{125}}\right)^{\frac{2}{3}} \\ =\left(\frac{125}{64}\right)^{\frac{2}{3}} =\left(\left(\frac{125}{64}\right)^{\frac{1}{3}}\right)^{2} =\left(\frac{125^{\frac{1}{3}}}{64^{\frac{1}{3}}}\right)^{2} \\ =\left(\frac{\sqrt[3]{125}}{\sqrt[3]{64}}\right)^{2} \\ =\left(\frac{\sqrt[3]{5^{3}}}{\sqrt[3]{4^{3}}}\right)^{2} \\ =\left(\frac{5}{4}\right)^{2} \\ =\frac{5^{2}}{4^{2}} \\ \left(\frac{64}{125}\right)^{-\frac{2}{3}}= \frac{25}{16}$$