Answer
$\frac{y^{15}}{8x^{12}}$
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, $(\frac{3y^{5}}{6x^{4}})^{3}=\frac{3^{3}(y^{5})^{3}}{6^{3}(x^{4})^{3}}=\frac{27(y^{5})^{3}}{216(x^{4})^{3}}$.
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, $\frac{27(y^{5})^{3}}{216(x^{4})^{3}}=\frac{27\times y^{5\times3}}{216\times x^{4\times3}}=\frac{27y^{15}}{216x^{12}}=\frac{y^{15}}{8x^{12}}$.
