Interesting. In our high school math class when -3^2 was hand written it was ok to interpret it as (-3)^2. But maybe that could have been because spacing would be used as some informal parentheses.
Leaving "-3²" to be "interpreted" according to context is not a good idea. Mathematical notation should be unambiguous and context-free as much as possible, not "do what I mean". A computation involving "-3²" will be right or wrong depending on what it means; that shouldn't depend on who is reading it or under what circumstances.
Not to unduly slight your teacher, but it could be they weren't sure about what "-3²" means. Everyone who teaches has gaps in their knowledge -- I sure did. :-)
Precedence rules are mostly a formalization of the underlying basic convention that the operations whose terms are written closer together are done first.
But if we’re doing math mostly on computers, we should adopt rules that make writing on computers easy — not pedantically insist typing code follow the rules of handwriting polynomials.
It was the same for me. The question seems to be whether "-3" here represents the operation "negate" or the number "negative 3". If it's the latter, then -3^2 is (-3)^2.
