Simplifying Question -- Please Help?

I have this problem to simplify with positive exponents:

http://img402.imageshack.us/img402/9...3bb9129099.png

So, working with the interior brackets, I applied -3 to the equation, which resulted in:

http://img856.imageshack.us/img856/7...407a55988f.png

**because "-4" was not in brackets, the exponent was applied to the 4 only, independent of the negative sign, which resulted in -(-64), so:

http://img545.imageshack.us/img545/1...f348e8da88.png

which resulted in this insane answer:

http://img341.imageshack.us/img341/1...21d92c8e8a.png

However, when I checked it, an online calculator said the answer was:

http://img802.imageshack.us/img802/8...a74bf7229a.png

which means that when applying exponents to the number I did something wrong, as it should have ended up negative, which would have resulted in it becoming a positive denominator.

What did I do wrong to end up with the wrong sign on that number?

Re: Simplifying Question -- Please Help?

Notice that $\displaystyle \displaystyle \begin{align*} (-4)^{-3} = \left[ (-4)^3 \right]^{-1} = -64^{-1} = -\frac{1}{64} \end{align*}$.

Re: Simplifying Question -- Please Help?

Awesome, thanks, I understand now! :D