Re: exponent
(-12)^-2 = ????
-12^-2 = ????
The basic rule is that the exponent operates only on the quantity immediately preceding it. Therefore 5^2 means 5 X 5 = 25 and -5^2 means the opposite of 5^2 or -(5 X 5) or -25.
So, if we want to square a "-5" we must put it in parenthesis so that the quantity immediately preceding the exponent is the quantity -5. Therefore (-5)^2 means (-5)X(-5) = +25.
In your case, you have a negative exponent to further confuse the issue. But the same rule applies.
(-5)^(-2) means \(\displaystyle \frac{1}{(-5)^2}=\frac{1}{25}\).
-5^(-2) means \(\displaystyle -\frac{1}{5^2}=-\frac{1}{25}\)
I should add that to avoid confusion the -2 exponent should also be enclosed in parenthesis giving us (-12)^(-2) and -12^(-2).
To further clarify (or confuse???) how would you evaluate the expression 100-5^2. Would you square a negative five then add, or would you square a positive 5 and subtract? You should get an answer of 75 rather than whatever else you might get.
