Answer
$ \frac{16a}{5b^{13}}$
Work Step by Step
$(125a^3b^9)^{-\frac{1}{3}}(4ab^{-5})^2$
=$[(125a^3b^9)^{-1}]^{ \frac{1}{3}} (\frac{4a}{b^5})^2$
=$[\frac{1}{ 125a^3b^9 }]^{\frac{1}{3}} (\frac{4a}{b^5})^2 $
=$[\frac{1}{ 5^3a^3(b^3)^3 }]^{\frac{1}{3}} (\frac{4a}{b^5})^2 $
=$[[\frac{1}{ 5a(b^3) }]^{3}]^{ \frac{1}{3}} (\frac{4a}{b^5})^2 $
=$\frac{1}{ 5ab^3 } (\frac{16a^2}{b^{10}}) $
=$\frac{16a^2}{5ab^{13}}$
=$\frac{16}{5}\frac{a^2}{a} \frac{1}{b^{13}}$
=$ \frac{16a}{5b^{13}}$