College Algebra (6th Edition)

$\frac{1}{1000x^{6}}$
When a product is raised to a power, raise each factor to that power: $$(10x^{2})^{-3}$$ $$=10^{-3}x^{(2\times(-3))}$$ $$=10^{-3}x^{-6}$$ Write as a fraction, move the base with the negative exponent to the other side of the fraction, and make the exponent positive: $$=\frac{1}{10^{3}x^{6}}$$ $$=\frac{1}{1000x^{6}}$$