\(\frac{27^3.15^5}{81^3.5^7}\)
\(=\frac{\left(3^3\right)^3.5^5.3^5}{\left(3^4\right)^3.5^7}\)
\(=\frac{3^9.3^5.5^5}{3^{12}.5^7}\)
\(=\frac{3^{14}.5^5}{3^{12}.5^7}\)
\(=\frac{3^2}{5^2}\)
\(=\frac{9}{25}\)
\(=5^{-4}\)
\(=\frac{1}{625}\)
\(\frac{27^3\cdot15^5}{81^3\cdot5^7}=\frac{\left(3^3\right)^3\cdot\left(3\cdot5\right)^5}{\left(3^4\right)^3\cdot5^7}=\frac{3^9\cdot3^5\cdot5^5}{3^{12}\cdot5^7}\)
\(=\frac{3^{14}\cdot5^5}{3^{12}\cdot5^7}\)
\(=\frac{3^2}{5^2}=\frac{9}{25}\)