Question

Tính :

\(A=\frac{2^{12}.27^3+20.6^9}{2.6^{10}+12^6.3^5}\)

Answer 1

\(A=\frac{2^{12}\cdot27^3+20\cdot6^9}{2\cdot6^{10}+12^6\cdot3^5}\)

\(=\frac{2^{12}\cdot\left(3^3\right)^3+2^2\cdot5\cdot2^9\cdot3^9}{2\cdot2^{10}\cdot3^{10}+\left(2^2\right)^6\cdot3^6\cdot3^5}\)

\(=\frac{2^{12}\cdot3^9+2^{11}\cdot5\cdot3^9}{2^{11}\cdot3^{10}+2^{12}\cdot3^{11}}\)

\(=\frac{2^{11}\cdot3^9\left(2\cdot5\right)}{2^{11}\cdot3^{10}\left(2\cdot3\right)}\)

\(=\frac{2^{11}\cdot3^9\cdot10}{2^{11}\cdot3^{10}\cdot6}\)

\(=3\cdot\frac{10}{6}=\frac{30}{6}=5\)