Answer
$\frac{-27b^{15}}{a^{18}}$
Work Step by Step
Start with the given expression: $(\frac{-15a^{4}b^2}{5a^{10}b^{-3}})^{3}$
Remove parentheses: $\frac{(-15)^3(a^4)^3(b^2)^3}{5^3(a^{10})^3(b^{-3})^3}$
Use power rule to simplify numerator and denominator: $\frac{-3375a^{12}b^{6}}{125a^{30}b^{-9}}$
Use quotient rule to simplify fraction: $-27a^{-18}b^{15}$
Use negative exponent rule to simplify completely: $\frac{-27b^{15}}{a^{18}}$
