\(\frac{9^9\cdot225^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}=\frac{9^9\cdot\left(\left(3\cdot5\right)^2\right)^5\cdot8^7}{\left(9\cdot2\right)^{12}\cdot\left(\left(5^2\right)^2\right)^3\cdot\left(8\cdot3\right)^3}\)
\(=\frac{1}{9^3\cdot2^{12}}\cdot\frac{9^5\cdot5^{10}}{5^{12}}\cdot\frac{8^7}{8^3\cdot3^3}\)
\(=\frac{9^2\cdot8^4}{2^{12}\cdot5^2\cdot3^3}\)
\(=\frac{9\cdot\left(2^4\right)^3}{\left(2^4\right)^3\cdot5^2}\)
\(=\frac{9}{25}\)