Math CentralQuandaries & Queries


Question from alex, a teacher:

I know that (-2)^2 is 4 but what is -2^2?

Hi Alex,

When I look at -22 I see two operations, a negation and a power (square). The convention in mathematical expressions is that powers are performed before negations (also before additions, multiplications and divisions) so to evaluate -22 you first square the 2 to get 4 and then apply the negation to arrive at -4.

With (-2)2 the parentheses tell you to consider -2 as a single quantity and square it so (-2)2 = (-2) × (-2) = 4.

I hope this helps,


It's -4.

Please note that this is not really a question (or answer) about arithmetic; it is about the convention that the second expression shall be interpreted as -(2^2). There is no deep mathematical reason for this; it has just been found to be more convenient. That said, now that the convention is established, we all need to follow it; it's like driving on the right (or left) side of the road.

Good hunting!

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS