Question

Tính :

\(\dfrac{5^2.6^11.(-16)^2+6^2.(-12)^6.(-15)^2}{2.(-6)^12.10^4-81^2.960^3}\)

Answer 1

\(=\dfrac{5^2\cdot6^{11}\cdot2^8+6^2\cdot6^6\cdot2^6\cdot15^2}{2\cdot6^{12}\cdot10^4-3^8\cdot2^{18}\cdot3^3\cdot5^3}\)

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

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

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

\(=\dfrac{1}{5}\cdot\dfrac{1}{8}\cdot\dfrac{1}{3}\cdot\dfrac{32\cdot3+1}{15-2}\)

\(=\dfrac{1}{120}\cdot\dfrac{97}{13}=\dfrac{97}{1560}\)