#### Answer

$a^2b^2c^{4}\sqrt[3]{bc}$

#### Work Step by Step

Extracting the factors that are perfect roots of the given index, the given expression, $
\sqrt[3]{a^6b^7c^{13}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{a^6b^6c^{12}\cdot bc}
\\\\=
\sqrt[3]{(a^2b^2c^{4})^3\cdot bc}
\\\\=
a^2b^2c^{4}\sqrt[3]{bc}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.