Answer
$-8p^{12}q^{6}r^{3}$
Work Step by Step
Based on the power of a product rule, we know that $(ab)^{n}=a^{n}b^{n}$ (where $n$ is a positive integer and $a$ and $b$ are real numbers).
Based on the power rule for exponents, we know that $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are positive integers and $a$ is a real number).
Therefore, $(-2p^{4}q^{2}r)^{3}=(-2)^{3}\times p^{4\times3}\times q^{2\times 3}\times r^{3}=-8p^{12}q^{6}r^{3}$.