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\(\dfrac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}\) \(=\dfrac{7.\left(2^2\right)^5+2^{13}.\left(3^3\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}\) \(=\dfrac{7.2^{10}.3^{11}+2^{13}.3^{15}}{2^{10}.3^{10}+2^{12}.3^{10}}\)

\(=\dfrac{7.2^{10}.3^{10}.3+2^{10}.2^3.3^{10}.3^5}{2^{10}.3^{10}+2^{10}.2^2.3^{10}}\) \(=\dfrac{2^{10}.3^{10}\left(7.3+2^3.3^5\right)}{2^{10}.3^{10}\left(1+2^2\right)}\)

\(=\dfrac{7.3+2^3.3^5}{1+2^2}\) \(=\dfrac{21+8.243}{5}\) \(=\dfrac{1965}{5}=393\)

\(\dfrac{7.4^5.3^{11}+2^{13}.9^5}{6^{11}+2^{12}.3^{10}}\)=\(\dfrac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{11}+2^{12}.3^{11}}\)=\(\dfrac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{11}.3^{11}+2^{12}.3^{11}}\)

= \(\dfrac{3^{10}.\left(7.3.2^{10}+2^{13}\right)}{3^{11}.\left(2^{11}+2^{12}\right)}\)=\(\dfrac{3^{10}.\left(21.2^{10}+2^{13}\right)}{3^{11}.\left(2^{11}+2^{12}\right)}\)=\(\dfrac{21.2^{10}+2^{13}}{3.\left(2^{11}+2^{12}\right)}\)

=\(\frac{7.\left(2^2\right)^5.3^{10}.3+2^{10}.2^3.\left(3^2\right)^5}{2^{10}.3^{10}+2^{10}.3^{10}.2^2}\)

=\(\frac{7.2^{10}.3^{10}.3+2^{10}.2^3.3^{10}}{2^{10}.3^{10}+2^{10}.3^{10}.2^2}\)

=\(\frac{2^{10}.3^{10}\left(7.3+2^3\right)}{2^{10}.3^{10}\left(1+2^2\right)}\)

=\(\frac{7.3+2^3}{1+2^2}\)

\(\frac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}=\frac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}=\frac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{10}.3^{10}+2^{12}.3^{10}}\)

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