\(\left(\dfrac{4}{25}\right)^2\cdot\left(\dfrac{2}{5}\right)^6:\left(-\dfrac{8}{125}\right)^3\)
\(=\left(\dfrac{2}{5}\right)^4\cdot\left(\dfrac{2}{5}\right)^6:\left(-\dfrac{2}{5}\right)^9\)
\(=\left(\dfrac{2}{5}\right)^{10}:\left(\dfrac{2}{5}\right)^9\cdot\left(-1\right)\)
\(=\left(\dfrac{2}{5}\right)\cdot\left(-1\right)=-\dfrac{2}{5}\)