Simplifying a ratio of powers This might sound like a stupid question but when it comes to simplifying when using the ratio test I get confused. Can someone please explain why $$\frac{2^{n+1}}{2^n}=\frac{2}{1}?$$ I think I might be thinking too hard because this confuses me.

Think about it this way. When you write $2^{n+1}$ you are multiplying a bunch of $2$s in sequence. Same for $2^n$. So if we write that as a bunch of $2$s:
(for $n=5$)
$\frac{2 * 2 * 2 * 2 * 2 * 2}{2 * 2 * 2 * 2 * 2}$
We can cancel out all of the 2s on the bottom and leave a single $2$ on top. And that single $2$ is the same as $2/1$.
