Question

[Nguyễn Lệ Ngân]

Rút gọn \(\frac{5^{2.}6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)

Answer 1

[duong bui]

em cũng chịu thôi khó quá 

Answer 2

[Vũ Hải Lâm]

Ta có: \(\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)

\(=\frac{5^2.2^{11}.3^{11}.2^8+2^2.3^2.3^6.2^{12}.5^2.3^5}{2.2^{12}.3^{12}.2^4.5^4-3^8.2^{18}.3^3.5^3}\)

\(=\frac{5^2.2^{19}.3^{11}+3^{13}.2^{14}.5^2}{2^{17}.3^{12}.5^4-2^{18}.3^{11}.5^3}\)

\(=\frac{\left(5^2.2^{14}.3^{11}\right)\left(2^5+3^2\right)}{\left(2^{17}.3^{11}.5^3\right)\left(3.5-2\right)}\)

\(=\frac{\left(2^5+3^2\right)}{\left(2^3.5\right)\left(3.5-2\right)}\)

\(=\frac{32+9}{40.13}\)

\(=\frac{41}{520}\)