Answer
$-27x^{3}y^{6}a^{9}$
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, $(-3xy^{2}a^{3})^{3}=(-3)^{3}\times x^{3}\times (y^{2})^{3}\times (a^{3})^{3}=-27\times x^{3}\times (y^{2})^{3}\times (a^{3})^{3}$.
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, $-27\times x^{3}\times (y^{2})^{3}\times (a^{3})^{3}=-27\times x^{3}\times y^{2\times3}\times a^{3\times3}=-27x^{3}y^{6}a^{9}$.