(\frac{9}{125})^3*(\frac{75}{81})^3=\frac{5^m}{3^n}
(\frac{3^2}{5^3})^3*(\frac{3*5^2}{3^4})^3=\frac{5^m}{3^n}
\frac{3^6}{5^9}*\frac{3^3*5^6}{3^{12}}=\frac{5^m}{3^n}
\frac{3^9*5^6}{5^9*3^{12}}=\frac{5^m}{3^n}
5^{6-9}*3^{9-12}=\frac{5^m}{3^n}
5^{-3}*3^{-3}=\frac{5^m}{3^n}
5^{-3}*\frac{1}{3^3}=\frac{5^m}{3^n}
\frac{5^{-3}}{3^3}=\frac{5^m}{3^n}
m= -3, n=3