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So, in the case here, what the calculators are giving you called the "principal root".
![khan academy calculus 2 khan academy calculus 2](https://i.ytimg.com/vi/tOX3RkH2guE/maxresdefault.jpg)
All it specifies is that there will always be three different roots. So, if you're interested in cube roots of a number (as you are in this example), you will always have three roots. When you take the nth root of a number, there are always n different roots In essence, the takeaway from it in the context of this problem is as follows: The reason comes from the Fundamental Theorem of Algebra. The 1 calculator that I found that showed a real solution was Symbolab. I know this is also the case for -5/3, try that on paper too. If you have any insight on the weirdness, please give me some insight below! Thanks for your time! :D I asked my math teacher and he said it should be real. But when you type in (-7/3)^(-7/3) onto most calculators, google included: I was finding y when x = -7/3 when I noticed something strange.
![khan academy calculus 2 khan academy calculus 2](https://i.ytimg.com/vi/I0MK7iOeAo4/maxresdefault.jpg)
I was using pencil and paper for most of my problems to determine whether the y values (given x) were real or not. Then I started to find as many points I could in the negative section to see if there was a pattern. This lead me to wonder whether there are points in between the integers, and there are! Such as when x = -1/3, yet not all are real numbers. I recognized that some values are complex and cannot be graphed, yet some can, such as (-1, -1) or (-2, 0.25).
![khan academy calculus 2 khan academy calculus 2](https://i.ytimg.com/vi/U2SQXHMqclc/maxresdefault.jpg)
I noticed the function abruptly stopped at the y-axis and did not extend into the second or third quatrains at all.
![khan academy calculus 2 khan academy calculus 2](https://i.ytimg.com/vi/sSyPAAyL8nQ/maxresdefault.jpg)
I'm not exactly good at math so forgive me if this question seems really silly.Ībout a week ago, I was wondering in my math class what the graph x^x looks like, and since we were using the desmos calculator in class, I tried it out. Don't have a question about this video, but I don't really have a good category to put it.
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