Tính:
\(\dfrac{3^6.45^4-15^{13}.\dfrac{1}{5^9}}{27^4.25^3+45^6}\)
\(=\dfrac{3^6.\left(3^2.5\right)^4-\left(3.5\right)^{13}.5^{-9}}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}\)
\(=\dfrac{3^6.3^8.5^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{13}.5^4.\left(3-1\right)}{2.3^{12}.5^6}\)
\(=\dfrac{3.2}{2.5^2}\)
\(=\dfrac{3}{25}.\)