Answer
$-24z^{20}$
Work Step by Step
Based on the product rule for exponents, we know that $a^{m}\times a^{n}=a^{m+n}$ (where $m$ and $n$ are positive integers and $a$ is a real number).
Therefore, $(4z^{10})(-6z^{7})(z^{3})=4\times-6\times z^{10+7+3}=-24\times z^{20}=-24z^{20}$.