Answer
$\frac{-27b^{30}}{a^{9}}$
Work Step by Step
Start with the given expression: $(\frac{-30a^{14}b^8}{10a^{17}b^{-2}})^{3}$
Remove parentheses: $\frac{(-30)^3(a^{14})^3(b^8)^3}{10^3(a^{17})^3(b^{-2})^3}$
Use power rule to simplify numerator and denominator: $\frac{-27000a^{42}b^{24}}{1000a^{51}b^{-6}}$
Use quotient rule to simplify fraction: $-27a^{-9}b^{30}$
Use negative exponent rule to simplify completely: $\frac{-27b^{30}}{a^{9}}$
