Answer
$\dfrac{25}{16}$
Work Step by Step
Use the rule $a^{-m}=\left(\dfrac{1}{a}\right)^m$.
$\left (-\dfrac{64}{125}\right )^{-\frac{2}{3}} =\left (-\dfrac{125}{64}\right )^{\frac{2}{3}} =\left (\dfrac{-125}{64}\right )^{\frac{2}{3}}$
Use $-125=(-5)^3$ and $64=4^3$.
$=\left (\dfrac{(-5)^3}{4^3}\right )^{\frac{2}{3}} $
Use the rule $\left(\dfrac{a}{b}\right)^n=\dfrac{a^m}{b^m}$:
$=\dfrac{\left((-5)^3\right)^{\frac{2}{3}}}{\left(4^3\right)^{\frac{2}{3}}} $
Use the rule $\left(a^m\right)^n=a^{mn}$, then simplify to obtain:
$=\dfrac{(-5)^2}{4^{2}}$
$=\dfrac{25}{16}$
Hence, the correct answer is $\frac{25}{16}$.
