Answer
$\frac{-27b^{15}}{a^{18}}$
Work Step by Step
$$(\frac{-15a^{4}b^{2}}{5a^{10}b^{-3}})^{3}$$
Group factors with like bases:
$$=[(\frac{-15}{5})(\frac{a^{4}}{a^{10}})(\frac{b^{2}}{b^{-3}})]^{3}$$
$$=[-3a^{(4-10)}b^{(2-(-3))}]^{3}$$
$$=[-3a^{-6}b^{(2+3)}]^{3}$$
$$=[-3a^{-6}b^{5}]^{3}$$
When raising a product to a power, raise each factor to that power:
$$=(-3)^{3}a^{(-6\times3)}b^{(5\times3)}$$
$$=-27a^{-18}b^{15}$$
Write as a fraction, move the base with the negative exponent to the other side of the fraction, and make the exponent positive:
$$=\frac{-27b^{15}}{a^{18}}$$
