Answer
$36x^{2}y^{2}z^{6}$
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, $(-6xyz^{3})^{2}=(-6)^{2}\times x^{2}\times y^{2}\times (z^{3})^{2}=36\times x^{2}\times y^{2}\times (z^{3})^{2}$.
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, $36\times x^{2}\times y^{2}\times (z^{3})^{2}=36\times x^{2}\times y^{2}\times z^{3\times2}=36x^{2}y^{2}z^{6}$.