Answer
$\frac{1}{16x^{6}}$
Work Step by Step
When a product is raised to a power, raise each factor to that power:
$$(4x^{3})^{-2}$$
$$=4^{-2}x^{(3\times(-2))}$$
$$=4^{-2}x^{-6}$$
Write as a fraction, move the base with the negative exponent to the other side of the fraction, and make the exponent positive:
$$=\frac{1}{4^{2}x^{6}}$$
$$=\frac{1}{16x^{6}}$$
