The two expressions -(a^6) and (-a^6) are the same. The ones you need to worry about are -(a^6) and (-a)^6.

Since the red negative sign doesn't show up in any parenthesis it is simply a constant factor out in front of everything. For the black negative sign think of it this way:

(-a^2 b^2)^3 = (-1)^3 * (a^2)^3 * (b^2)^3 = -(a^2)^3 * (b^2)^3

which is again outside of everything. So you got it right.

-Dan