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

\(=\dfrac{\left(2^2\right)^6.\left(3^2\right)^5_{\cdot}+\left(2.3\right)^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)

\(=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}\)

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

\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}\)

\(=\dfrac{2^{13}.3^{11}}{2^{11}.3^{11}.5}\)

\(=\dfrac{2^2}{5}\)

\(=\dfrac{4}{5}\)

=3627970560

=1813985280

\(\frac{10.4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2.5.\left(2.2\right)^6.\left(3.3\right)^5+\left(2.3\right)^9.3.40}{\left(2.2.2\right)^4.3^{12}-\left(2.3\right)^{11}}=\frac{2.5.2^6.2^6.3^5.3^5+2^9.3^9.3.40}{2^4.2^4.2^4.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{13}.5.3^{10}+2^{12}.5.3^{10}}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.5.3^{10}.\left(2+1\right)}{2^{11}.3^{11}\left(2.3-1\right)}=\frac{2^{12}.5.3^{11}}{2^{11}.5.3^{11}}=2\)

\(\dfrac{10.4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{5.2.2^{12}.3^{10}+3^9.2^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\dfrac{5.2^{13}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}=\dfrac{2^{12}.3^{10}.5\left(2+1\right)}{2^{11}.3^{11}.5}\)

\(=\dfrac{2^{11}.2.3^{10}.5.3}{2^{11}.3^{10}.3.5}=2\)

4⁶.9⁵+6⁹.120 / 8⁴.3¹²-6¹¹

=(2²)⁶.(3²)⁵+(2.3)⁹.2³.3.5 / (2³)⁴.3¹²-(2.3)¹¹

=2¹².3¹⁰+2⁹.3⁹.2³.3.5 / 2¹².3¹²-2¹¹.3¹¹

=2¹².3¹⁰+2¹².3¹⁰.5 / 2¹¹.3¹¹.(2.3-1)

=2¹².3¹⁰.(1+5) / 2¹¹.3¹¹.(6-1)

=2¹².3¹⁰.6 / 2¹¹.3¹¹.5

=2¹³.3¹¹ / 2¹¹.3¹¹.5

=2²/5

=4/5

4/5 chắc chắn luôn

\(\frac{8^4.3^{12}-6^{11}}{4^9.9^5+6^9.120}\)Dề thế này à

chịu

\(=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}+2^{11}\cdot3^{11}}=\dfrac{2^{13}\cdot3^{11}}{2^{11}\cdot3^{11}\cdot7}=\dfrac{4}{7}\)