Question

How do you simplify $\frac{1}{x^{-2}}$?

Answer 1

Simplify the expression $\frac{1}{x^{-2}}$:

Apply the rule of exponents, $a^{-m}=\frac{1}{a^m}$ in the given expression,

$\begin{array}{rcl}\frac{1}{x^{-2}}& =& \frac{1}{{\displaystyle \frac{1}{x^2}}}\\ & \Rightarrow & \frac{1}{x^{-2}}=1\times \frac{x^2}{1}\\ & \Rightarrow & \frac{1}{x^{-2}}=x^2\end{array}$

Thus, the given expression is simplified as $x^2$.