Find the values of $m$ and $n$ for which $\int_{0}^{1} x^n\exp{(-mx)}dx$ converges.

I need to find the values of $m$ and $n$, so that the following integral converges:$$\int_{0}^{1} x^n\exp{(-mx)}dx$$My attempt:Case-1:If $n\ge0$ then the given integral is proper integral irrespective of $m$ and hence convergent.
Case-2:If $n<0$ then $0$ is the point of infinite discontinuity,so it will become an improper integral.Now i want to use comparison test for convergence of this integral.In a text book it is given that:
In $[0,1]$, $x^n\exp(-mx)\le kx^n$,for some $k>1$ and $\forall m$.I am unable to verify this inequality and also i do not know other way to solve this problem.
Kindly help me.