Couldn't resist:

but when multiplications are denoted by juxtaposition, as in 4c ÷ 3ab

Damn, and I thought they were called "products" not "multiplications" 🤔🤔🤔

No it doesn’t. If you meant ab², then you would just write ab². If you’ve written a(b)², then you mean (a×b)²

If you can find an explicit textbook example where writing a(b)² is said to be evaluated as (a×b)² then that's another way you can prove your good faith (When I say "explicit" I don't mean it must literally be that formula; the variables a and b could have different names, or could be constants written with numerals, and the exponent could be anything other than 1). Likewise, if you can find any explicit textbook example which specifically mentions an "exception" to the distributive law, that would demonstrate good faith.

I'm not saying that such an explicit example is the only way to demonstrate your claim, but I'm just trying to give you more opportunities to prove that you're not just a troll and that it's possible to have a productive discussion. You insist you're talking about mathematical rules that cannot be violated, so it should be no problem to find an explicit mention of them.

If you think this insistence on demonstrating your good faith is unfair, you should remember that you are saying that the practice of calculators, mathematical tools, programming languages and mathematical software are all wrong and that you are right, and that my interpretation of your own textbooks is wrong. While it's not impossible for many people to be wrong about something and for me to interpret something wrong, if you show no ability to admit error, or to admit that disagreement from competing authorities casts doubt on your claims, or to evince your controversial claims with explicit examples that are not subject to interpretational contortions, the likelihood is that you're not willing to ever see truth and there's no point arguing with such a person.

By the way, sorry for making multiple replies on the same point.

As my own show of good faith, I do see that one of your textbooks (Chrystal) has the convention that a number "carries with it" a + or -, which is suppressed in the case of a term-initial positive number. If you demonstrate it worth continuing the discussion, I'll explain why I think this is a bad convention and why the formal first-order language of arithmetic doesn't have this convention.

So when you sneer that rules and notation are different, you don't know what those words mean.

Or you're so devoid of internality that when someone says 'imagine a different notation,' you literally can't.

There’s no pretending, It’s there in the textbooks

Show me any textbook that gets the answers you insist on. Show me one textbook where a(b+c)^2^ squares a.