TITLE: $-3^2 = 9?\ $ Correct syntax for a negative number with an exponent.
QUESTION [29 upvotes]: A friend is taking a college algebra class and they are teaching him that 
$$-3^2 = -9$$
Their explanation is:
$$-3^2 = -(3^2) = -9.$$
It has been a long time for me but I thought that in the absence of any parenthesis that:
$$-3^2 = (-3) \times (-3) = 9.$$
They are even contradicting themselves because they teach the odd/even shortcut for exponents in another part of the book. i.e.:
if the exponent is even, the result it positive, and if
 the exponent is odd the result is negative. 

This is an actual picture of the book where they contradict themselves on the $-3^2 = -9$:

edit
OK, since this has generated way more attention then I ever imagined I've updated here to respond to some of the comments. 
1) I understand why the book is not contradicting itself in the picture specifically, or even in the "odd/even" exponent context, due to the fact that variable substitution always implies parens. The book and the teacher, from what my friend has said, do not do a good job of explaining that distinction though. 
2) Yes, I understand why the answer is that $-3^2$ is NOT ambiguous is due to order of operations. 
3) I made a comment about Khan Academy teaching it incorrectly, I realized I was wrong once I re-watched the video.

REPLY [4 votes]: To round out the answers, one might wonder why we chose to order operations so that $-3^2$ means $-(3^2)$ rather than $(-3)^2$.
A very simple reason is that if we mean to say $(-3)^2$, we have an alternate — and simpler — way to express the same value that we would prefer to use in most circumstances: $3^2$
However, if we mean to say $-(3^2)$, we don't have a correspond alternative.
Thus, the convention where $-3^2$ means $-(3^2)$ is simply more useful than the alternative.