Answer
$$(5x^{2}y^{-4})^{-3} = \frac{ y^{12}}{125x^{6}}$$
Work Step by Step
$$(5x^{2}y^{-4})^{-3}$$
Recall the product-to-power rule: $(ab)^n$ =$a^{m}b^{n}$ and power rule: $(a^{m})^{n}=a^{mn}$
Thus,
$$(5x^{2}y^{-4})^{-3}$$ $$5^{-3}x^{2(-3)}y^{-4(-3)}$$ $$5^{-3}x^{-6}y^{12}$$
Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$
Thus,
$$5^{-3}x^{-6}y^{12}$$ $$\frac{ y^{12}}{5^{3}x^{6}}$$ $$\frac{ y^{12}}{125x^{6}}$$
