Answer
$$9|x|$$
Work Step by Step
RECALL:
(1) For any real numbers $a \ge 0, b\ge0$, $\sqrt{ab}=\sqrt{a} \cdot \sqrt{b}$.
(2) For any real numbers $a \ge 0, b\gt 0$, $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$.
(3) $\sqrt{a^2}=|a|$
Use rule (1) above to obtain:
\begin{align*}
\sqrt{81x^2}&=\sqrt{81}\cdot \sqrt{x^2}\\
&=9\sqrt{x^2}
\end{align*}
Use rule (3) above to obtain:
\begin{align*}
9\sqrt{x^2}&=9 \cdot |x|\\
&=9|x|
\end{align*}