Mathematics question on products, factorials and summation

Hi, i'm an undergraduate, and theres something my lecturor has gone through that i don't quite understand.

it's this below:

I understand the 'pi' means products of, i also understand how he's seperated out the products, but i don't understand where the power comes from and i don't understand where the factorial comes from

- thanks in advance

Sum 2m x 2m x .... 2m n terms so 2 x 2 x 2 n times which is 2 ^ n

The facorial comes as m goes from 1 to n so 1 x 2 x 3 x 4 ..... x n = n!