Answer
$\frac{y^{3}}{27x^{12}}$
Work Step by Step
$$(\frac{3x^{4}}{y})^{-3}$$
When raising a quotient to a power, raise both the numerator and denominator to the power:
$$=\frac{(3x^{4})^{-3}}{y^{-3}}$$
When raising a product to a power, raise each factor to that power:
$$=\frac{3^{-3}x^{(4\times(-3))}}{y^{-3}}$$
$$=\frac{3^{-3}x^{-12}}{y^{-3}}$$
Move the base with the negative exponent to the other side of the fraction, and make the exponent positive:
$$=\frac{y^{3}}{3^{3}x^{12}}$$
$$=\frac{y^{3}}{27x^{12}}$$
