tl;dr with exponents like this is that negative signs are bad, get rid of them.
You can write this as:
[tex]( \frac{1}{4ab})^{-1})^{^2}[/tex]
Anything to the -1 involves flipping the fraction, so we now simplify this to:
[tex]( \frac{4ab}{1}) ^2=(4ab)^2[/tex]
Now we know with exponents outside of the bracket, it's the same as writing the bracket out twice, which means everything is multiplied by everything, i.e. in this case we multiply 4ab by 4ab which means we square everything.
Therefore
[tex](4ab)^2=4^2a^2b^2 \\ \\ \boxed{=16a^2b^2}[/tex]
