No matter how you look at it, there's going to be HUGE opinion regarding this. You're always taught that multiplication supercedes addition/subtraction. But, in this case, it looks as though you have a problem. The order of operations states that it's left to right unless a supercede interrupts the process, thus eliminating rules until the operation takes place, putting order back to left to right. In this case, we have -2^2, but with it as is, and everyone not wanting to interpret it in any fancy order: (-2)^2, (0 - 2)^2, 0 - 2 ^ 2, or whatever else you can think of, it's simply a matter of everyone's opinion, including mine. If you were to ask me, I would have to explain as follows:
-2^2 - A number that is already labeled negative must stay there, because if we go on to changing things the way we want (0 - 2), in my opinion, we screw up the whole mathematical system. The equations must be interpretted as they are written. So, in this case, have negative 2 squared 2 times, -2^2. So, following the order of operations' alloted cases where multiplication supercedes any other form of calculation, you must identify that this equation is multiplying a negative number twice, which allows you to end up with a positive. I'm stating this as OPINION because that's what it is. I could be wrong, or I could be right, it's all opinion. You can't say, well this is (-2)^2, because that is NOT how this operation is written. If there is a rule that will allow you to write just that, then I think that is the missing link that we are searching for. If you slice it, you see (-2)^2, -(2)^2. Either way, your negative attachment is superceding the multiplication because it is a multiplication in itself. You are negotiating the point of whether the number is positive or negative, which is noted as an operation of importance to that of multiplication/division, so this MUST be concluded before any multiplication is done. Why? Order of operations tells us that it is to be performed left to right, unless an operation of higher law/imporance is apparent before that calculation can take place, in which case those operations are performed beforehand, left to right of course. Once those operations have been done, you can continue with normal left->right operation. In this case, however, we have 2 cases where left->right has the same rule of operation as each other.
Anyhow, I'm open to other suggestions that heed incorrect on this. Sorry for the long post ;-)
