Show that $\int_{\pi/2}^{3\pi/2}\frac{e^{\alpha+Re^{i\theta}}}{(\alpha+Re^{i\theta})^p}iRe^{i\theta}d\theta \to 0$ as $R\to\infty$, for $\alpha, p>0$?

Question

Essentially I want to show that

$$\lim_{R\to \infty}\int_C\frac{e^{z}}{z^p}dz=0$$

Where $C$ is a semi circle with radius $R$ centered at the fixed real value $\alpha>0$ (the semi circle is to the left of the centre). The semi circle is oriented in the anticlockwise direction and $p>0$.

Hence after making a substitution $z=\alpha +Re^{i\theta}$ it's clear that we get the integral in the question:

$$\int_{\pi/2}^{3\pi/2}\frac{e^{\alpha+Re^{i\theta}}}{(\alpha+Re^{i\theta})^p}iRe^{i\theta}d\theta$$

I'm now not sure I where I would go from here? I could expand $e^{\alpha+Re^{i\theta}}=1+\alpha+Re^{i\theta}+\frac{1}{2}(\alpha+Re^{i\theta})^2+...$

But I can't see how I'd manipulate this to show that the denominator tends to $\infty$ faster than the numerator?