Ta có:

\(\frac{2^{20}\cdot27^3+30\cdot4^9\cdot9^4}{6^9\cdot4^5+12^{10}}=\frac{2^{20}\cdot\left[3^3\right]^3+2\cdot3\cdot5\cdot\left[2^2\right]^9\cdot\left[3^2\right]^4}{2^9\cdot3^9\cdot\left[2^2\right]^5+3^{10}\cdot\left[2^2\right]^{10}}=\frac{2^{20}\cdot3^{3\cdot3}+2\cdot3\cdot5\cdot2^{2\cdot9}\cdot3^{2\cdot4}}{2^9\cdot3^9\cdot2^{2\cdot5}+3^{10}\cdot2^{2\cdot10}}\)

\(=\frac{2^{20}\cdot3^9+2\cdot3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+3^{10}\cdot2^{20}}=\frac{2^{20}\cdot3^9+2^{19}\cdot3^9\cdot5}{2^{19}\cdot3^9+3^{10}\cdot2^{20}}=\frac{2^{19}\cdot3^9\left[2+5\right]}{2^{19}\cdot3^9\left[1+3\cdot2\right]}=\frac{2+5}{1+6}=\frac{7}{7}=1\)

là 1 nha bạn

\(\dfrac{2^{20}.27^3+30.4^9.9^4}{6^9.4^5+12^{10}}=\dfrac{2^{20}.3^9+3.2.5.2^{18}.3^8}{2^9.3^9+2^{10}+2^{20}.3^{10}}\)

\(=\dfrac{2^{19}.3^9.\left(2+5\right)}{2^9.3^9.\left(1+2^{11}.3\right)+2^{10}}=\dfrac{2^{10}.\left(2+5\right)}{1+2^{10}.\left(2.3+1\right)}\)

\(=\dfrac{2^{10}.7}{2^{10}.7+1}=\dfrac{7168}{7169}\)

Chúc bạn học tốt!!!

\(\dfrac{2^{20}.27^3+30.4^9.9^4}{6^9.4^5+12^{10}}=\dfrac{2^{20}.3^9+2.3.5.2^{18}.3^8}{2^9.3^9+2^{20}.3^{10}}=\dfrac{2^{20}.3^9+5.2^{19}.3^9}{2^9.3^9+2^{20}.3^{10}}=\dfrac{2^9.3^9\left(2^{11}+5.2^{10}\right)}{2^9.3^9\left(1+2^{11}.3\right)}\)

\(\dfrac{2^{11}+5.2^{10}}{1+2^{11}.3}\)

tới bc này chiu :))

giúp mk ik, năn nỉ đó.

\(=\dfrac{2^{19}\cdot3^9-3\cdot3^8\cdot2^{18}\cdot5}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}=\dfrac{-3^{10}\cdot2^{18}}{2^{19}\cdot3^9\cdot7}=-\dfrac{3}{14}\)

\(H=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)

\(H=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)

\(H=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)

\(H=\frac{2^{19}.3^9+2^{18}.5.3^9}{2^{19}.3^9+2^{20}.3^{10}}\)

\(H=\frac{2^{18}.3^9.\left(2+5\right)}{2^{19}.3^9.\left(1+2.3\right)}\)

\(H=\frac{2^{18}.3^9.7}{2^{19}.3^9.\left(1+6\right)}\)

\(H=\frac{2^{18}.3^9.7}{2^{19}.3^9.7}=\frac{1}{2}\)

\(K=\frac{4^7.2^8}{3.2^{15}.16^2-5.2^2.\left(2^{10}\right)^2}\)

\(K=\frac{\left(2^2\right)^7.2^8}{3.2^{15}.\left(2^4\right)^2-5.2^2.2^{20}}\)

\(K=\frac{2^{14}.2^8}{3.2^{15}.2^8-5.2^{22}}\)

\(K=\frac{2^{22}}{3.2^{23}-5.2^{22}}\)

\(K=\frac{2^{22}}{2^{22}.\left(3.2-5\right)}=\frac{2^{22}}{2^{22}.1}=1\)

`@` `\text {Ans}`

`\downarrow`

\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=\dfrac{2^3}{1}=2^3=8\)

_____

\(\dfrac{4^8\cdot9^4}{6^6\cdot8^3}\)

`=`\(\dfrac{\left(2^2\right)^8\cdot\left(3^2\right)^4}{2^6\cdot3^6\cdot\left(2^3\right)^3}\)

`=`\(\dfrac{2^{16}\cdot3^8}{2^6\cdot3^6\cdot2^9}\)

`=`\(\dfrac{2^{16}\cdot3^8}{2^{15}\cdot3^6}\)

`=`\(\dfrac{3^2}{2}\) `=`\(\dfrac{9}{2}\)

______

\(\dfrac{27^4\cdot2^3-3^{10}\cdot4^3}{6^4\cdot9^3}\)

`=`\(\dfrac{\left(3^3\right)^4\cdot2^3-3^{10}\cdot\left(2^2\right)^3}{2^4\cdot3^4\cdot\left(3^2\right)^3}\)

`=`\(\dfrac{3^{12}\cdot2^3-3^{10}\cdot2^6}{2^4\cdot3^4\cdot3^6}\)

`=`\(\dfrac{3^{10}\cdot\left(3^2\cdot2^3-2^6\right)}{3^{10}\cdot2^4}\)

`=`\(\dfrac{72-2^6}{2^4}=\dfrac{8}{16}=\dfrac{1}{2}\)

\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=2^3=8\)

\(\dfrac{4^8.9^4}{6^6.8^3}=\dfrac{2^{16}.3^8}{2^6.3^6.2^9}=2.3^2=18\)

\(\dfrac{27^4.2^3-3^{10}.4^3}{6^4.9^3}=\dfrac{3^{12}.2^3-3^{10}.2^6}{2^4.3^4.3^6}=\dfrac{2^3.3^{10}.\left(3^2-2^3\right)}{2^4.3^{10}}=\dfrac{9-8}{2}=\dfrac{1}{2}\)

\(=\dfrac{2^{19}\cdot3^9+2^{18}\cdot3^9\cdot5}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}=\dfrac{2^{18}\cdot3^9\left(5+2\right)}{2^{19}\cdot3^9\left(1+2\cdot3\right)}=\dfrac{1}{2}\)

\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)

\(=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}\)

\(=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^{19}.3^9+3^{10}.2^{20}}\)

\(=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+3.2\right)}\)

\(=\frac{7}{2.7}=\frac{1}{2}\)