This is probably quite simple but I am not sure where to start, any help appreciated!
[(4a^-2)^-2]^-1
Let's use the formula: x^-n= 1/(x^n). We shall start with outer exponent: 1/[(4a^-2)^-2]^1=1/(4a^-2)^-2. Follow the same formula = 1/{1/(4a^-2)^2. Fraction divide by fraction= fraction multiply by reciprocal; (4a^-2)^2, let's simplify this; 16a^-4, and one more negative exponent: 16/a^4