why is (-6)^-1 a negative answer and (-1?2)^-2 positive?

Chris, the minus on the second one is NOT inside the bracket :/

Oh I see the confusion.

The heading and the question are different.

I did the question in the body of the post and CPhill did the question in the heading.

Remember that :   a^-n = 1/aⁿ

So (-6)^-1  =  1/-6 = -(1/6)

And (-1/2)^-2  =  1 / (-1/2)²  =   1/ [ (-1/2) * (-1/2)] = 1 / (1/4)  = 4

$$\\(-6)^{-1}=\frac{1}{(-6)^1}=\frac{1}{-6}=-\frac{1}{6}\\\\\\
-\left(\frac{1}{2}\right)^{-2}
=-\left(\frac{2}{1}\right)^{+2}
=-\frac{2^2}{1^2}
=-4$$

So they are both negative.  Does that help or do you want to quiz me about it?

Added later:  Oh i will do the heading one too

$$\left(\frac{-1}{2}\right)^{-2}
=\left(\frac{2}{-1}\right)^{+2}
=\frac{2^2}{(-1)^2}
=\frac{2*2}{-1*-1}
=\frac{4}{1}
=4$$