\(\dfrac{2}{3}\) nha

\(A=\dfrac{2.2^{12}.3^8+2^2.2^9.3^9}{2^7\left(2^7.3^7+2^3.5.3^8\right)}=\dfrac{2^{13}.3^8+2^{11}.3^9}{2^7\left(2^7.3^7+2^3.5.3^8\right)}\)

\(A=\dfrac{2^{11}.3^8\left(2^2+3\right)}{2^7.2^3.3^7\left(2^4+5.3\right)}\)

\(A=\dfrac{2.3.7}{31}=\dfrac{42}{31}\)

\(\frac{2.2^{12}.3^6+2^2.2^9.3^9}{2^7.2^7.3^7.2^4.5.3^8}\)

\(=\frac{2^{13}.3^6+2^{11}.3^{^9}}{2^{18}.3^{15}.5}\)

\(=\frac{2^{11}.3^6\left(2^2+3^3\right)}{2^{11}.3^6.2^6.3^4.5}\)

\(=\frac{35}{2^6.3^4.5}\)

\(B=\dfrac{2\cdot2^{12}\cdot3^6+2^2\cdot2^9\cdot3^9}{2^7\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot3^8}\)

\(=\dfrac{2^{13}\cdot3^6+2^{11}\cdot3^9}{2^{14}\cdot3^7+2^{10}\cdot5\cdot3^8}\)

\(=\dfrac{2^{11}\cdot3^6\left(2^2+3^3\right)}{2^{10}\cdot3^7\left(2^4+5\cdot3\right)}=\dfrac{2}{3}\cdot\dfrac{31}{31}=\dfrac{2}{3}\)

\(A=\frac{2\cdot\left(2^3\right)^4\cdot\left(3^3\right)^8+2^2\cdot\left(2\cdot3\right)^9}{2^7\cdot6^7+2^7\cdot\left(2^3\cdot5\right).\left(3^2\right)^4}\)

\(A=\frac{2\cdot2^{12}\cdot3^{24}+2^2\cdot\left(2\cdot3\right)^9}{12^7+2^7\cdot\left(2^3\cdot5\right)\cdot3^8}\)

Đến đó thì bí

hihi

đến đó thì bt rồi

a, \(\dfrac{2\cdot8^4\cdot27^2+4\cdot6^9}{2^7\cdot6^7+2^7\cdot40\cdot9^4}\)

=\(\dfrac{2\cdot\left(2^3\right)^4\cdot\left(3^3\right)^2+2^2\cdot2^9\cdot3^9}{2^7\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot\left(3^2\right)^4}\)

=\(\dfrac{2\cdot2^{12}\cdot3^6+2^{11}\cdot3^9}{2^{14}\cdot3^7+2^{10}\cdot5\cdot3^8}\)

=\(\dfrac{2^{11}\cdot3^6\cdot\left(2^2+3^3\right)}{2^{10}\cdot3^7\cdot\left(2^4+5\cdot3\right)}\)

=\(\dfrac{2^{11}\cdot3^6\cdot31}{2^{10}\cdot3^7\cdot31}\)

=\(\dfrac{2}{3}\)

b, \(\dfrac{\dfrac{8}{27}\cdot\dfrac{9}{16}\cdot\left(-1\right)}{\dfrac{4}{25}\cdot\dfrac{-125}{1728}}\)

=\(\dfrac{\dfrac{8\cdot9\cdot\left(-1\right)}{27\cdot16}}{\dfrac{4\cdot\left(-125\right)}{25\cdot1728}}\)

=\(\dfrac{\dfrac{-1}{6}}{\dfrac{-5}{432}}\)

=\(\dfrac{-1}{6}\cdot\dfrac{-432}{5}\)

=\(\dfrac{72}{5}\)