If the local maximum value of the function $f(x)=\left(\dfrac{\sqrt{3}e}{2\sin x}\right)^{\sin^{2}x},; x\in\left(0,\dfrac{\pi}{2}\right),$ is $\dfrac{k}{e},$ then $\left(\dfrac{k}{e}\right)^{8}+\dfrac{k^{8}}{e^{5}}+k^{8}$ is equal to: