Application Of Derivatives

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