Why do equations in these forms always intersect the point $(1,1)$?

Question

I was fooling around with a graphing calculator, and I discovered something that surprised me a little. Suppose I have a quadratic equation in the following form, where $n \in \mathbb{R}$:

$$y=x^n$$

Now, if I graph this, again, assuming that $n \in \mathbb{R}$, the resulting line will always intersect the point $(1,1)$. I found this to be, interesting to say.

In addition, I've also observed that this happens with the following equation as well.

$$ y = \sqrt[n]{x} \\ $$

Is there an explanation as to why this is the case? Is there anything special in particular about the point $(1,1)$?

Answer 1

To make my comment an answer in the hopes that future generations won't wonder why we left so many open questions:

$1=1^r$ for every $r\in\mathbb{R}$.