Answer
$\frac{x^{3}y^{12}}{-27z^{9}}$
Work Step by Step
Based on the power of a quotient rule, we know that $(\frac{a}{c})^{n}=\frac{a^{n}}{c^{n}}$ (where $n$ is a positive integer and $a$ and $c$ are real numbers).
Therefore, $(\frac{xy^{4}}{-3z^{3}})^{3}=\frac{x^{3}(y^{4})^{3}}{(-3)^{3}(z^{3})^{3}}=\frac{x^{3}(y^{4})^{3}}{-27(z^{3})^{3}}$.
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, $\frac{x^{3}(y^{4})^{3}}{-27(z^{3})^{3}}=\frac{x^{3}\times y^{4\times3}}{-27\times z^{3\times3}}=\frac{x^{3}y^{12}}{-27z^{9}}$.