Answer
$-2a^{4}\sqrt[3]{10a^2}$
Work Step by Step
Extracting the factors that are perfect roots of the given index, the given expression, $
\sqrt[3]{-80a^{14}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{-8a^{12}\cdot 10a^2}
\\\\=
\sqrt[3]{(-2a^{4})^3\cdot 10a^2}
\\\\=
-2a^{4}\sqrt[3]{10a^2}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.