rules for why -3^-2 = 1/9 but (-3)^2 = -1/9

[vanpritch016]

Okay I have these 2 questions and I have the answers to them but I don't understand how you get the second answer if anyone can enlighten me.

problem 1: -3 ^ -2

i know you flip that so you get an absolute value......which turns this to 1/ -3 ^ 2 and the answer becomes 1/9 because -3 x -3 gives you positive 9 but now

problem 2 ---which is similar: (-3) ^2

it says the answer is -1/9 and I dont understand how it becomes negative because if you multiply 2 negatives you get a positive.... obviously theres some sort of rule that I'm unaware of.. so if someone can help me i'd appreciate it.

 

[galactus]

Re: need help with negative power problem

I am not following because \(\displaystyle (-3)^{2}=9\)

 

[skeeter]

Re: need help with negative power problem

recheck your "answers" along with the original problem. The following are correct ...

\(\displaystyle -3^2 = -1 \cdot 3^2 = -9\)

\(\displaystyle -3^{-2} = -\frac{1}{3^2} = -\frac{1}{9}\)

\(\displaystyle (-3)^2 = (-1 \cdot 3)^2 = (-1)^2 \cdot 3^2 = 1 \cdot 9 = 9\)

\(\displaystyle (-3)^{-2} = \frac{1}{(-3)^2} = \frac{1}{9}\)

 

[vanpritch016]

Re: need help with negative power problem

Skeeter,

thanks alot!! and your right I had the answers backwards.