I can rephrase if you like: Why does -5^2=-25 without parens, but -5!
needs parens to get -120? Or if you prefer: Why is -5^2 NOT ambiguous, but -5! is? (I'm don't believe -5! really is ambiguous by the way)
Your question is one of interpretation. Difficulties of interprettation can be entirely avoided simply by using brackets. But for some unfathomable reason, students just don't want to do this. In fact, students get quite stroppy when told to do this. And even stroppier when their work is misunderstood. And often it is themselves that misunderstand their own work ....
Just use brackets!
if I want to answer it I will consider it like this
maybe another one consider it like this
so if you use brackets you will remove the misunderstanding for the problem
so it is important to use brackets
-5^2=-25 (at least to me!). Looking unusual is not the criteria for deciding if () are needed. I know many (non math students) people who would find 3+4x2=11 VERY UNUSUAL. Their surprise at the answer of 11 does not obligate me to include parens.
My question is simple. Just like from a strict order of operations point of view, 3+4x2=11 WITHOUT parens, I want to what is -5! Don't put in parens. Just tell me what it equals.