Question 8517: I do not understand why -3² = -9 when (-3)² = 9
I know a negative times a negative equals a positive. So how can -3x-3= -9?
Found 2 solutions by Earlsdon, prince_abubu:
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Look at it this way.
(-3)^2 = (-3)*(-3) = 9 You are correct in saying that a negative times a negative gives a positive result as you can see here.
-3^2 = -(3*3) = -(3)^2 = -(9) Here, you have a positive times a positive gives a positive result but the whole thing has a negative sign in front so that makes the result negative.
Answer by prince_abubu(198) (Show Source):
You can put this solution on YOUR website!  is due to the order of operations. Remember that it goes "Parentheses, Exponents, Multiplication/Division, Addition/Subtraction" from "strongest force" to "weakest force".
If there are, for example, three numbers that have forces between them (in this case, a force can be the plus, minus, multiplication sign, division sign, or an indication to raise to a power), the stronger force will be computed first. For example, take 3*5 + 7. The force between the 3 and 5 is multiplication. The force between the 5 and 7 is addition. Since the force between the 3 and the 5 (aka, the multiplication) is stronger than the addition force between the 5 and the 7, the 3 * 5 will be computed first to get the 15. Only then would there be the addition force between the 15 and the 7. Since there are no stronger forces than the lone addition, the 15 and 7 will add together to 22.
The same principle works with the example . That equation really is saying  . Since the force between the 3 and the 2 (the exponent force) is stronger than the multiplication force between the -1 and the 3, the  is calculated first and you get the 9. This brings you down to -1*9, which is -9.
With the  , we have the parentheses which acts like something that "breaks the rules" of the "force order". In this case, the parentheses dictates to unify a weaker force (the multiplication force between -1 and 3) FIRST before performing the supposedly more powerful (in this case) exponent force.
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