Question

[phamphuckhoinguyen]

Tính

A= 20.4^14.9^9-4.9^10.8^9/40.2^6.6^19-7.2^29.27^6

Answer 1

[Trí Tiên亗]

\(A=\frac{20\cdot4^{14}\cdot9^9-4\cdot9^{10}\cdot8^9}{40\cdot2^6\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)

\(=\frac{2^2\cdot5\cdot2^{28}\cdot3^{18}-2^2\cdot3^{20}\cdot2^{27}}{2^3\cdot5\cdot2^6\cdot2^{19}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)

\(=\frac{2^{30}\cdot3^{18}\cdot5-2^{29}\cdot3^{20}}{2^{28}\cdot3^{19}\cdot5-2^{29}\cdot3^{18}\cdot7}\)

\(=\frac{2^{29}\cdot3^{18}\left(2\cdot5-3^2\right)}{2^{28}\cdot3^{18}\cdot\left(3\cdot5-2\cdot7\right)}\)

\(=\frac{2^{29}\cdot3^{18}}{2^{28}\cdot3^{18}}=2\)

Vậy : \(A=2\)