Answer
$6y^{5}x^2z$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
-\sqrt[3]{-216y^{15}x^6z^3}
,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers.
$\bf{\text{Solution Details:}}$
Expressing the radicand of the expression above with a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
-\sqrt[3]{(-6y^{5}x^2z)^3}
\\\\=
-(-6y^{5}x^2z)
\\\\=
6y^{5}x^2z
.\end{array}