A Built-In Hierarchy

The order isn't random — it follows a hierarchy of operations. Exponents are repeated multiplications, and multiplications are repeated additions. Resolving the most compressed form first keeps arithmetic consistent with that stacking, which is why parentheses (your override) come before everything else.

That is also why machines never argue about it. Every modern programming language — Python, JavaScript, Excel — hard-codes PEMDAS into its parser and treats the rule as the one thing nobody negotiates.