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I've been given a long limit problem to solve and i got stuck on this part in the question. Could someone please give me hints or suggestions on where to go next?

Given that [tex]\frac{e^{x}}{x^{n}}[/tex] > e[tex]^{x - n\sqrt{x}}[/tex]

Find the [tex]lim_{x\rightarrow+\infty}[/tex] [tex]\frac{e^{x}}{x^{n}}[/tex]

Well i know that [tex]lim_{x\rightarrow\infty}[/tex] e[tex]^{x}[/tex] = [tex]\infty[/tex]

but i think the question would like us to use the inequality above.

Any help would be greatly appreciated :)