\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)
\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.2^9.3}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{25}.5^{12}}\)
\(=\frac{3^3.1.1}{1.1.5^2}\)
\(=\frac{27}{25}\)