I have this problem to simplify with positive exponents:

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

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

which resulted in this insane answer:

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

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?

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