Answer
$2x^2z^4\sqrt{2x}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt{8x^5z^8}
,$ use the laws of exponents to simplify the radicand. Then, find a factor of the radicand that is a perfect power of the index. Finally, extract the root of the factor that is a perfect power of the root.
$\bf{\text{Solution Details:}}$
Factoring the expression that is a perfect power of the index and then extracting the root result to
\begin{array}{l}\require{cancel}
\sqrt{4x^4z^8\cdot2x}
\\\\=
\sqrt{(2x^2z^4)^2\cdot2x}
\\\\=
|2x^2z^4|\sqrt{2x}
.\end{array}
Since all variables are assumed to be positive, then,
\begin{array}{l}\require{cancel}
2x^2z^4\sqrt{2x}
.\end{array}
