Find the likelihood function of $f(x)=e^{-(x-a)- e^{-(x-a)}}$
I know the definition and I know it should look like $$\mathcal L(a)=f(x_1\mid a)\dots f(x_n\mid a)$$ but I'm lost with the exponential calculation, can someone show me the likelihood function of this thing? I got it like $$\mathcal L(a)=\exp\left\{{-\sum_{i=1}^{n} x_i-a-e^{-\sum_{i=1}^{n} x_i-a}}\right\}$$ can it be simplier?