I have been teaching a long time, and I know from experience that 50% of students will tell me that –3^2 = +9 on a test or a final, despite having discussed it a few times in a course.

When I first started teaching I taught calculus and precalc. Piece of cake. Then I started with an Algebra I class and couldn’t connect at all for the first week or so. I was ready to believe I couldn’t teach. I simply could not explain how I got the right answers when evaluating expressions... Then I discovered the order of operations (PEMDAS to some). A definition of the order of operations which I had so internalized that I didn’t know there was a rule for it. Since that discovery I’ve been a wonderful teacher. :-)

So... I must be missing something that so many of my students think –3^2 is +9. What is the rule I have never discovered?

Full disclosure: I think –k^2, k a constant, should be banned from mathematics texts and tests. -x^2, x a variable, evaluated for say –3, absolutely (no pun intended) but not –3^2.

Phil