I've got the following question in a stats paper, just a bit stuck on how they get their answer:

Suppose that the random variable follows the exponential distribution , with p.d.f.

for , 0 otherwise.

Find the find the k-th moment of X, i.e. , for some positive integer .

I know that this is , and also that the Gamma Distribution of is defined as , just not sure how to relate the two.

Thanks in advance for any help