Question

[Nam Lee]

Tính :

5² . 6¹¹ . (-16)² + 6² . (-12)⁶ . (-15)² / 2 . (-6)¹² . 10⁴ - 81² . 960³ .

Answer 1

[Nguyễn Lê Phước Thịnh]

\(=\dfrac{5^2\cdot6^{11}\cdot2^8+6^2\cdot6^6\cdot2^6\cdot3^2\cdot5^2}{2\cdot6^{12}\cdot10^4-3^8\cdot2^{18}\cdot3^3\cdot5^3}\)

\(=\dfrac{5^2\cdot3^{11}\cdot2^{19}+2^8\cdot2^6\cdot3^8\cdot3^2\cdot5^2}{2^{13}\cdot3^{12}\cdot5^4\cdot2^4-3^{11}\cdot2^{18}\cdot5^3}\)

\(=\dfrac{5^2\cdot3^{11}\cdot2^{19}+2^{14}\cdot3^{10}\cdot5^2}{2^{17}\cdot3^{12}\cdot5^4-3^{11}\cdot2^{18}\cdot5^3}\)

\(=\dfrac{5^2\cdot3^{10}\cdot2^{14}\left(3\cdot2^5+1\right)}{2^{17}\cdot3^{11}\cdot5^3\left(3\cdot5-2\right)}\)

\(=\dfrac{1}{5}\cdot\dfrac{1}{3}\cdot\dfrac{1}{8}\cdot\dfrac{96+1}{13}=\dfrac{97}{5\cdot3\cdot8\cdot13}\)