a)\(\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}=\frac{3^6.\left(3^2.5\right)^4-\left(3.5\right)^{13}.5^{-9}}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}=\frac{3^6.3^8.5^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)

\(=\frac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+3^{12}.5^6}=\frac{3^{13}.5^4.\left(3-1\right)}{3^{12}.5^6\left(1+1\right)}=\frac{3^{13}.5^4}{3^{12}.5^6}=\frac{3}{5^2}=\frac{3}{25}\)

b)\(\frac{4^6.9^5+6^9.120}{-8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5}{-\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{-2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{-2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{-\left(2^{12}.3^{12}+2^{11}.3^{11}\right)}=\frac{2^{12}.3^{10}\left(1+5\right)}{-\left[2^{11}.3^{11}\left(2.3+1\right)\right]}=\frac{2.6}{-\left(3.7\right)}=\frac{4}{-7}\)

\(\frac{10^3+2.5^3+5^3}{55}-\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)\(=\frac{2^3.5^3+2.5^3+5^3}{5.11}-\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\frac{5^3\left(2^3+2+1\right)}{5.11}-\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{5^2.11}{11}-\frac{2.6}{3.5}=25-\frac{4}{5}=\frac{121}{5}\)

\(=-\dfrac{2^{12}\cdot3^{10}+3^9\cdot2^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}+2^{11}\cdot3^{11}}\)

\(=-\dfrac{2^{12}\cdot3^{10}+3^{10}\cdot2^{12}\cdot5}{2^{11}\cdot3^{11}\cdot7}\)

\(=-\dfrac{3^{10}\cdot2^{12}\cdot6}{2^{11}\cdot3^{11}\cdot7}=-\dfrac{2}{3}\cdot\dfrac{6}{7}=\dfrac{-12}{21}=-\dfrac{4}{7}\)

giúp mk với

bài này khó quá!

giúp nha

thanks

Đầu tiên ta rút gọn \(\frac{4^{^6}.9^{^5}+6^{^9}.120}{8^{^4}.3^{^{12}}-6^{^{11}}}\)= \(\frac{2^{^{12}}.3^{^{10}}+2^{^9}.3^{^9}.2^{^3}.3.5}{2^{^{12}}.3^{^{12}}-2^{^{11}}-3^{^{11}}}\)= \(\frac{2^{^{12}}.3^{^{10}}+2^{^{12}}.3^{^{10}}.5}{2^{^{12}}.3^{^{12}}-2^{^{11}}.3^{^{11}}}\)= \(\frac{2^{^{12}}.3^{^{10}}.\left(1+5\right)}{2^{^{11}}.3^{^{11}}.\left(6-1\right)}\)= \(\frac{2.6}{3.5}\)= \(\frac{12}{15}\)= \(\frac{4}{5}\)

\(\Rightarrow\)10 . \(\frac{4}{5}\)= \(\frac{40}{5}\)= 8

\(=\dfrac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot5}=\dfrac{2}{3}\cdot\dfrac{6}{5}=\dfrac{12}{15}=\dfrac{4}{5}\)

Ta có : \(A=\frac{4^6.9^5+6^9.120}{-8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+2^9.3^9.2^3.3.5}{-\left(2^3\right)^4.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{-2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(-2.3-1\right)}=\frac{2\left(1+5\right)}{3\left(-6-1\right)}=\frac{2.6}{3.\left(-7\right)}=\frac{-12}{21}\)

Bằng -4/7 ghe bạn