\(\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(=\dfrac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^5}-\dfrac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{125^3.7^3+5^9.\left(7.2\right)^3}\)
\(=\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{\left(5^3\right)^3.7^3+5^9.7^3.2^3}\)
\(=\dfrac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}-\dfrac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3\left(1+2^3\right)}\)
\(=\dfrac{2}{3.4}-\dfrac{5.\left(-6\right)}{1+8}\)
\(=\dfrac{2}{12}-\dfrac{-30}{9}\)
\(=\dfrac{1}{6}+\dfrac{10}{3}\)
\(=\dfrac{1}{6}+\dfrac{20}{6}\)
\(=\dfrac{21}{6}\)
\(=\dfrac{7}{2}\)
