Question

\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)

Answer 1

\(\frac{4^6+9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)

\(=\frac{2.6}{3.5}=\frac{4}{6}\)

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Answer 2

\(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)

\(=\frac{2.6}{3.5}\)

\(=\frac{4}{5}\)