given that

X|M=m \epsilon Exp{m} with M^(-1) \epsilon GAMMA{p,a}

show X has a (translated) pareto distribution.

I tried something like this:

\integral 1/m Exp{-x/m} 1/f_m(x) with f_m(x)= 1/gamma(p)*x^(p-1)*1/(a^p)*Exp(-x/a)

but i got stuck in the mess and did not get any pareto like distribiion