Why is $ |x-\mu|^\alpha+|x-\mu|^n=\Theta(|x|^n)$ at $x \to \infty$?

Question

I'm currently studying a proof and don't see why the following holds true.

Let $n \ge \alpha > 0, I \subseteq \mathbb R$ and $x, \mu \in I$.

Why is \begin{equation*} |x-\mu|^\alpha+|x-\mu|^n=\Theta(|x|^n)\end{equation*} at $x \to \infty$?

And also why do we have \begin{equation*} |x-\mu|^\alpha+|x-\mu|^n=\Theta(|x-\mu|^\alpha)\end{equation*} at $x \to \mu$?