How to evaluate this integral $\int_0^∞ ax^me^{-{ax}^n} dx$

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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 ?