I don't really get exponents with a negative base...How do they work?

Question

For example, my math teacher(algebra 2) stated that -3^2=-9. On a calculator, this isn't quite true, but I have a feeling my teacher is right. Shouldn't -3x-3=9? Could anyone grant me some clarification upon this? Thanks in advance!

Answer 1

you square first, then multiply by -1, this is not (-3)² but (-1) 3²

Answer 2

It depends on how the algebra statement is made. If your math teacher said that (-3)^2 = -9, then that is incorrect. Any real number squared (multiplied by itself) produces a positive number. Perhaps the teacher intended to say that -(3)^2 = -9. This would be correct, since 3^2 = 9 and -(3^2) = -9.

Answer 3

it is a matter of what is squared.  If you are squaring the (-3) it is +9, but if it is written as -3^2 it is understood that the 3 is being multiplied with a -1 and you are only doing -1(3^2) because the square is only of the one unit.