Answer
$-27x^{21}y^{3}z^{6}$
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).
Therefore, $(-3x^{7}yz^{2})^{3}=(-3)^{3}\times (x^{7})^{3}\times y^{3}\times (z^{2})^{3}=-27\times (x^{7})^{3}\times y^{3}\times (z^{2})^{3}$.
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, $-27\times (x^{7})^{3}\times y^{3}\times (z^{2})^{3}=-27\times x^{7\times3}\times y^{3}\times z^{2\times3}=-27x^{21}y^{3}z^{6}$.
