saying that -4^2 = (-4)^2 is just lazy and careless math.
Yeah but as I said before writing -4^2=-1(4^2) is lazy as well. Why can't they write it down fully?
My point is that it's not obvious to like half(or most) people that the "-" sign in -4^2 is not part of the "4". If you just look at this writing most people would assume it's a -4 with exponential, because it looks like it. In this example :"3+4+9-4^2" it's pretty clear that the 4^2 is a different operation and have the higher priority over the others, but if it's on it's own like in the question people easily assume it's -4*-4.
Not to mention the fact that most calculators and teachers say the same. No wonder people are confused about this.
I think the problem could be easily solved by putting the parentheses there in both examples. I know -4^2 is shorter than -1(4^2) but it would save many people from headaches.