Question

How do you simplify ${\left(ab\right)}^{-2}$?

Answer 1

Simplify the expression:

The negative exponent rule is defined as $\frac{1}{x^{-a}}=x^a$, where $x,a$ are any real numbers.

and by the exponent rule, we have ${\left(ab\right)}^n=a^n{b}^n$.

Using the exponent rules to simplify the expression.

$$\begin{gathered} {\left(ab\right)}^{-2}=\frac{1}{{\left(ab\right)}^2} \\ \therefore {\left(ab\right)}^{-2}=\frac{1}{a^2{b}^2} \end{gathered}$$

Hence, ${\left(ab\right)}^{-2}$ is equal to $\frac{1}{a^2{b}^2}$.