It’s not that hard.
If you have -3 -3s and I give you one, you now only have -2 -3s. If you want to get to a total of -6, I have to hand over 4 more -3s to get there, the first 3 of them just being what’s needed to get you to 0 and out of deficit. Now you get to hold onto the next two I hand over, and now you have 2 -3s which total -6. But that’s 15 worth of -3s I had to hand over to get you there and -6 + 15 = 9, like -3 × -3 does too.
Negative numbers aren “real”. Like 0, they’re just a concept used to represent something, deficit.
Lmao not gonna lie, this would be a very intuitive way of teaching a kid negative values.
Fun fact: exponents and multiplication DO work like rotation … in the complex domain (numbers with their imaginary component). It’s not a pure rotation unless it’s scalar, but it’s neat.
I know I explained that the worst ever, but 3blue1brown on YT talks about it and many other advanced math concepts in a lovely intuitive way.