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So from what I am thinking, would it be wrong to think that in the equation -3^2 = -9, then the dash in front of the 3 is a subtraction symbol. So if we have subtraction a dash symbol and negative numbers a superscript dash symbol, then the dash in front of 3 would be a regular dash and the dash in front of 9 would be superscript dash.

So it would seem that if the dash in front of 3 were superscript, then the answer would be positive 9.

There aren't different types of dash symbols. You only have two types.

1) Substraction. This is a binary operation between two numbers. Like ##3-9## and ##1-1##.

2) Negative of a number. This is a unary operation on one number, like ##-3##.

The two are linked by ##0-x=-x## and ##x-y = x+(-y)##.

So ##-3^2## can be seen as ##0-3^2## if you want, but the result is still ##-9##. The only way you can get this to yield ##9## is by inserting brackets.