(\frac{81}{125})^4 \cdot (\frac{75}{9})^3 = \frac{3^m}{5^n}
L=P
{L=(\frac{81}{125})^4 \cdot (\frac{75}{9})^3 =(\frac{3^4}{5^3})^4 \cdot (\frac{3\cdot 5^2}{3^2})^3 = \frac{3^{16}}{5^{12}} \cdot \frac{3^3 \cdot 5^6}{3^6}=\frac{3^{16}\cdot 3^3 \cdot 3^{-6}}{5^{12} \cdot 5^{-6}}=\frac{3^{16+3-6}}{5^{12-6}}=\frac{3^{13}}{5^{6}}}
\frac{3^{13}}{5^{6}}=\frac{3^m}{5^n}
m = 13
n = 5