Answer
$$\frac{−27b^{30}}{a^{9}}$$
Work Step by Step
$$(\frac{−30a^{14}b^{8}}{10a^{17}b^{-2}})^{3}$$
Recall the power rule: $(a^{m})^{n}=a^{mn}$
Thus,
$=(\frac{−30a^{14}b^{8}}{10a^{17}b^{-2}})^{3}$
$=(\frac{−3a^{14}b^{8}}{a^{17}b^{-2}})^{3}$$=\frac{−3^{3}a^{14\cdot 3}b^{8\cdot 3}}{a^{17\cdot 3}b^{-2\cdot 3}}$
$=\frac{−27a^{42}b^{24}}{a^{51}b^{-6}}$
Recall the quotient rule: $\frac{a^{m}}{a^{n}}=a^{m-n}$ and $\frac{a^{n}}{a^{m}}=\frac{1}{a^{m+n}}$ if $m>n$
Thus,
$=\frac{−27a^{42}b^{24}}{a^{51}b^{-6}}$
$=\frac{−27b^{24+6}}{a^{51-42}}$
$=\frac{−27b^{30}}{a^{9}}$
