Negative exponent is a reciprocal

How to use it

1. 1Unwind a nested expression from the innermost bracket outwards, replacing each $-1$ power by the reciprocal of what it encloses.
2. 2${\left(\frac{1}{x^2}\right)}^{-\frac{1}{2}}=(x^2{)}^{\frac{1}{2}}$: negate the exponent, keep the base.
3. 3A minus sign in a numerator can be carried to the denominator when inverting.

Step-by-step

1. 1
   ${\left(\frac{3}{4}\right)}^{-1}=\frac{4}{3}$

   Why: Invert the innermost bracket first.

2. 2
   $1-\frac{4}{3}=-\frac{1}{3}$
3. 3
   ${\left(-\frac{1}{3}\right)}^{-1}=-3$