Derivation of Product of First n Terms of Geometric Progression

The product of the first $n$ terms of a Geometric Progression is given by the following:
 

Given the first term $a_1$ and last term $a_n$:

$P_n = \sqrt{(a_1 \times a_n)^n}$

 

Given the first term $a_1$ and the common ratio $r$

$P_n = {a_1}^n \times r^{n(n - 1)/2}$