Assuming α is known, find the maximum likelihood estimator of β

f(x;α,β) =, 1 ,,,,,,,.(x^{α}.e^{-x/β)}

,,,,,, ,,,,,,α!β^{α+1}

I know that firstly you must take the likelihood of L(β). But unsure if I have done it correctly. I came out with the answer below, please can someone tell me where/if I have gone wrong.

L(β)= (α!β^{α+1})^{-n}.Σxi^{α}.e^{Σxi/βn}