Can I write $(\pm(5\cdot\frac{4}{5}), 0)$ to indicate the points $(4,0)$ and $(-4,0)$? Is putting brackets inside of the brackets indicating an ordered pair allowed, i.e I'm asking if putting brackets around $5\cdot\frac{4}{5}$ in $(\pm(5\cdot\frac{4}{5}), 0)$ allowed or not.
It'd be awfully helpful if I was allowed to write like this.
On
Formally speaking yes it is fine, indeed $(\pm5\times4/5,0)=(\pm4,0)$, but the former is unclean and unorderly, so writing in the simplest form is always the cleanest, unless of course you are showing in some computation that the former is the same as the latter, in which case it’s an explanation for the reader.
That's allowed. You can use parentheses wherever you like to group arithmetic operations. That said, it's hard to parse. It would be easier if you were not also using parentheses for the vector.
In this particular case, $\pm(4,0)$ or $(\pm4, 0)$ would be much better.
In general, your goal choosing notation should be to help your reader.