Answer
$2abc^3\sqrt[3]{b^2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt[3]{8a^3b^5c^9}
,$ write the radicand as an expression that contains a factor that is a perfect power of the index. Then extract the root of that factor.
$\bf{\text{Solution Details:}}$
Writing the radicand as an expression that contains a factor that is a perfect power of the index and extracting the root of that factor result to
\begin{array}{l}\require{cancel}
\sqrt[3]{8a^3b^3c^9\cdot b^2}
\\\\=
\sqrt[3]{(2abc^3)^3\cdot b^2}
\\\\=
2abc^3\sqrt[3]{b^2}
.\end{array}
