đợi mình xíu 

\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)

\(\Leftrightarrow\frac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)

\(\Leftrightarrow\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)

\(\Leftrightarrow\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{13}.3^{13}-2^{11}.3^{11}}\)

\(\Leftrightarrow\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.2^{12}-2^{11}.2^{11}}\)

\(\Leftrightarrow\frac{2^{12}.3^{10}.\left(1+5\right)}{6^{12}-6^{11}}\)

\(\Leftrightarrow\frac{2^{12}.3^{10}.6}{6^{11}.\left(6-1\right)}\)

\(\Leftrightarrow\frac{2^{12}.3^{10}.2.3}{6^{11}.\left(6-1\right)}\)

\(\Leftrightarrow\frac{2^{13}.3^{11}}{6^{11}.5}\)

\(\Leftrightarrow\frac{2^{11}.3^{11}.2^2}{6^{11}.5}\)

\(\Leftrightarrow\frac{6^{11}.4}{6^{11}.5}\Leftrightarrow\frac{4}{5}\)

4⁶ . 9⁵ + 6⁹ . 120 / 8⁴ . 3¹² - 6¹¹

= ( 2² )⁶. ( 3² ) ⁵ + (2 . 3 ) ⁹ . 2³ . 3 . 5 / ( 2³ ) ⁴ . 3¹² - ( 2 . 3 ) ¹¹
= 2^12.3^10+2^9.3^9.2^3.3.5 / 2^12.3^12-2^11.3^11
= 2^12.3^10+2^12.3^10.5 / 2^11.3^11.(2.3-1)
= 2^12.3^10.(1+5) / 2^11.3^11. (6-1)
= 2^12.3^10.6 / 2^11.3^11.5
= 2^13.3^11 / 2^11.3^11.5
= 2^2/5
=4/5

\(\frac{7}{6}+\frac{5}{6}:5-\frac{3}{8}.\left(-3\right)^2\)

\(=\frac{7}{6}+\frac{5}{6}.\frac{1}{5}-\frac{3}{8}.9\)

\(=\frac{7}{6}+\frac{1}{6}-\frac{27}{8}\)

\(=\frac{8}{6}-\frac{27}{8}\)

\(=\frac{32}{24}-\frac{81}{24}\)

\(=\frac{-49}{24}\)

Chúc bạn học tốt !!!