Question

Tìm số đó :

\(\dfrac { 4^6 . 9^5 + 6^9 . 120 } { 8^4 . 3^{12} - 6^{11}}\)

Answer 1

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

\(=\dfrac{\left(2^2\right)^6.\left(3^2\right)^5_{\cdot}+\left(2.3\right)^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)

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

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

\(=\dfrac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(6-1\right)}\)

\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}\)

\(=\dfrac{2^{13}.3^{11}}{2^{11}.3^{11}.5}\)

\(=\dfrac{2^2}{5}\)

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