My textbook makes a calculation and just says "with some simplications", and then gets the answer.

We have L0=(1/sqrt(2pi))^n*(e^(-1/2*sum(xi-m0)^2)...i.e. this the max likelihood function for a normal with variance 1 and mean m0. Sum is from 1 to n. We have L1 is the same except replace m0 with m1.

Then they compute L0/L1 and get

e^((n/2)*(m1^2-m0^2)+(m0-m1)*sum(xi))

I do not see where this step comes from. Any ideas?

Thank you.