If the local maximum value of the function f(x)=((√(3 e))/(2 sin x))^sin^2 x, x ∈(0, (π)/2), is k/e, then (k/e)^8+k^8/e^5+k^8 is equal to

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