Subtle Proof Error I'm having trouble seeing the error in the following "proof":
$$ (-4)=(-4)^1=(-4)^\frac{2}{2}=[(-4)^2]^\frac{1}{2}=[16]^\frac{1}{2}=4$$ therefore $(-4)=4$. 
Obviously this is incorrect, but I'm not seeing where the error is occuring. I appreciate any help. Thanks.

$x^{\frac{1}{2}}$ gives two values, both additively inverse to each other, on all nonzero real numbers $x$. You can think of an equation like $2^\frac{1}{2} = \pm \sqrt{2}$ as saying that the square root of $2$ is "$\sqrt{2}$ or $-\sqrt{2}$."
