Answer
$7|c|$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of radicals and absolute value to simplify the given expression, $
\sqrt{(-7c)^2}
.$
$\bf{\text{Solution Details:}}$
Since $\sqrt{x^2}=|x|$ for any real value $x,$ the expression above simplifies to
\begin{array}{l}\require{cancel}
\sqrt{(-7c)^2}
\\\\=
|-7c|
.\end{array}
Since $|cx|=|c|\cdot|x|$ where $c$ is a constant, then
\begin{array}{l}\require{cancel}
|-7c|
\\\\=
|-7|\cdot|c|
\\\\=
7|c|
.\end{array}
