?Why does −32=−9 but (−3)2=9

With respect to proof (rather than just a tautology of the mathematical statement like "it's opposite").


Part of it is the notational convention regarding precedence of operations.  When you fully parenthesize  −32  you get  −(32).

The other part is the rule of signs.  A negative number times a negative number is a positive number, so  (−3)2  is a positive number, but of course, −(32)  is a negative number.

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