It should be read as the opposite of 3 squared. Since 3 squared is 9, the opposite is -9. The "-" sign is used in 3 different ways. In front of a natural number it means negative or minus, in front of anything else it means opposite and between two things it means add the opposite.
________________________________ From: firstname.lastname@example.org [email@example.com] on behalf of Guy Brandenburg [firstname.lastname@example.org] Sent: Thursday, October 18, 2012 6:04 AM To: email@example.com; Philip Mahler Cc: mathedcc Subject: Re: Please remind me why -3^2 = -9
It's a convention. In a case like that, one really ought to use parentheses to make the meaning clear, since a lot of people, not just youngsters, will get confused.
If one intends to say (-3)*(-3), then write (-3)^2. If one means - (3)*(3), then write - (3^2).
-3 means -1 x 3, so -3^2 is (-1)(3^2) = (-1)(9) = -9.
________________________________ From: "Philip Mahler" <firstname.lastname@example.org> To: "mathedcc" <email@example.com> Sent: Thursday, October 18, 2012 5:37:07 AM Subject: Please remind me why -3^2 = -9
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.