I decided to review the properties of expontents after posting a question and getting downvoted. The answer was easy; however, got a bit confused by $ n^{x^m} $ with $n,m \in \mathbb{Z}$
So I started with the most basic thing I could think of and that is to draft a picture.
I am stuck at drawing the graph of $x^y$ at $(0,0)$. Getting confused about how to take the limit to the right and left of this. Which limit do I take first, the limit of $x$ as it goes to zero or the limit of $y$ as it goes to zero, from either the right or left.
Yes, I type $x^y$ into Wolfram Alpha, however, don't understand why the first is a 3D picture and the second picture doesn't show good the point $(0,0)$. I am just deducing a guess that the two different colors on oppositite quadrants mean there are 4 cases.
I do realize the graph will contain all the 2D plane. (sorta like a slope field).
My guess and its not strong, the point $(0,0)$ doesn't exist. I have tried searching online, but from what I could understand from the articles I read (most are above my knoweldge of math), is that there are three possible values $0,1$, and DNE.