Trying to solve it using the gamma function
$ax^me^{-u} = u \times (\frac{u^{\frac{1}{n}}}{a^{\frac{1}{n}}})^{m – n-n +1}$
I actually used the fact that
$ax^n \times ax^{m-n} = ax^m$
so $u = ax^n$
$dx = \frac{du}{nax^{n-1}}$
So that's how $-n+1$ comes in
I take $a^{\frac{-m}{n} +1 - \frac{1}{n}}$ out of the integral
Note : I multiplied -1 to the power because i were to move the inverse of it outside the integral
I am left with $n^{-1} a^{\frac{-m}{n} +1 - \frac{1}{n}}\int_0^∞ u^{\frac{m}{n} -1 + \frac{1}{n}} e^{-u}du$
So I actually I need the gamma function for $\frac{m}{n} + \frac{1}{n}$ and multiply it with the constants ?