There is a standard, I’m not claiming there isn’t

Ah ok. Sorry, got caught out by a double negative in your sentence.

Confusion exists because operating against the standard doesn’t immediately break everything like ignoring brackets would

Ah but that's exactly the original issue in this thread - the e-calc is ignoring the rules pertaining to brackets. i.e. The Distributive Law.

Ah ok. Well that was my only confusion was what you had actually intended to write, not how to interpret it (depending on what you had intended). Yes should be interpreted 2^81.

including Excel

Yeah, but Excel won't let you put in a factorised term either. It's just severely broken because the people who wrote it didn't bother checking the rules of Maths first. Programmers not knowing the rules of Maths doesn't mean Maths is ambiguous (it certainly creates a lot of confusion though!).

We have a standard because it’s ambiguous. If there was only one way to do it, we’d just do that,

Disagree. There is one way to do it - follow the rules of Maths. That's why they exist. The order of operations rules are at least 400 years old, and make it not ambiguous. If people aren't obeying the rules then they're just wrong - that doesn't make it ambiguous. It's like saying if e-calcs started saying 1+1=3 then that must mean 1+1 is ambiguous. It might create confusion, but it doesn't mean the Maths is ambiguous.