Answer
$3b^2\sqrt[3]{a}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[3]{27ab^6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{27b^6\cdot a}
\\\\=
\sqrt[3]{(3b^2)^3\cdot a}
\\\\=
3b^2\sqrt[3]{a}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.