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

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

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

\(=\frac{2^{19}.3^9.\left(1+5\right)}{2^{19}.3^9.\left(1+2.3\right)}=\frac{6}{7}\)

st sai 1/2 mới đúng

\(=\frac{2^{19}.3^9+3^9.5.2^{18}}{2^9.3^9.2^{10}+2^{20}.3^{10}}=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{1}{2}\)

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

= \(\frac{2^{19}.3^9+5.2^{18}.3^9}{6^9.2^{10}+2^{10}.6^{10}}\)

=\(\frac{\left(2^{18}.3^9\right)\left(2+5\right)}{\left(6^9.2^{10}\right)\left(1+6\right)}\)

=\(\frac{7\left(2^{18}.3^9\right)}{7\left(3^9.2^9.2^{10}\right)}\)

= \(\frac{7\left(2^{18}.3^9\right)}{7\left(3^9.2^{19}\right)}\)

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

\(=\dfrac{2^{19}\cdot3^9+2^{18}\cdot3^9\cdot5}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}=\dfrac{2^{18}\cdot3^9\cdot\left(2+5\right)}{2^{19}\cdot3^9\cdot7}=\dfrac{1}{2}\)

Ta có:

\(\frac{2^{19}.27^9+15.4^9.9^4}{6^9.2^{12}+12^{10}}=\frac{2^{19}.\left(3^3\right)^9+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{12}+\left(2^2.3\right)^{10}}\)

\(=\frac{2^{19}.3^{27}+3.5.2^{18}.3^8}{2^9.3^9.2^{12}+2^{20}.3^{10}}=\frac{2^{19}.3^{27}+3^9.2^{18}.5}{2^{21}.3^9+2^{20}.3^{10}}=\frac{2^{18}.3^9.\left(2.3^{18}+5\right)}{2^{20}.3^9.\left(2+3\right)}\)

\(=\frac{1.1.\left(2.3^{18}+5\right)}{2^2.1.5}=\frac{2.3^{18}+5}{20}\)

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

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

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

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

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

\(A=1.\frac{2+5}{2+4.3}\)

\(A=\frac{7}{14}=\frac{1}{2}\)

Vậy \(A=\frac{1}{2}\)

\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+3^{10}.2^{20}}=\frac{2^{18}.3^9\left(2+5\right)}{2^{18}.3^9\left(2+3.2^2\right)}=\frac{7}{14}=\frac{1}{2}\)