We are given the following expression:
[tex](ab)^{-2}[/tex]
First, we will use the following property of exponentials:
[tex](xy)^{-c}=x{}^{-c}y^{-c}[/tex]
Applying the property we get:
[tex](ab)^{-2}=(a^{-2})(b^{-2})[/tex]
Now, we use the following property of exponentials:
[tex]x^{-c}=\frac{1}{x^c}[/tex]
Applying the property we get:
[tex](a^{-2})(b^{-2})=\frac{1}{(a^2)(b^2)}=\frac{1}{(ab)^2}[/tex]
Since we can't simplify any further this is the final answer.
