Answer
$=\frac{-27b^{30}}{a^{9}}$
Work Step by Step
$$(\frac{-30a^{14}b^{8}}{10a^{17}b^{-2}})^{3}$$
Group factors with like bases:
$$=[(\frac{-30}{10})(\frac{a^{14}}{a^{17}})(\frac{b^{8}}{b^{-2}})]^{3}$$
$$=[-3a^{(14-17)}b^{(8-(-2))}]^{3}$$
$$=[-3a^{-3}b^{(8+2)}]^{3}$$
$$=[-3a^{-3}b^{10}]^{3}$$
When raising a product to a power, raise each factor to that power:
$$=(-3)^{3}a^{(-3\times3)}b^{(10\times3)}$$
$$=-27a^{-9}b^{30}$$
Write as a fraction, move the base with the negative exponent to the other side of the fraction, and make the exponent positive:
$$=\frac{-27b^{30}}{a^{9}}$$
