Rút gọn A= 2^19 x 27^3 + 15 x 4^9 x 9^4  / 6^9 x 2^10 + 2^10

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\(=\dfrac{2^{19}.\left(3^3\right)^3-3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}=\dfrac{2^{19}.3^9-5.2^{18}.3^9}{2^{19}.3^9+2^{20}.3^{10}}=\dfrac{2^{18}.3^9\left(2-5\right)}{2^{19}.3^9\left(1+6\right)}=\dfrac{-3}{2.7}=-\dfrac{3}{14}\)

\(=-\dfrac{3}{14}\)

\(=\dfrac{2\cdot3^9+3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+2^{20}\cdot3^{10}}=\dfrac{2\cdot3^9+3^9\cdot2^{18}\cdot5}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}\\ =\dfrac{2\cdot3^9\left(1+2^{17}\cdot5\right)}{2^{19}\cdot3^9\left(1+2\cdot3\right)}=\dfrac{1+2^{17}\cdot5}{2^{18}\cdot7}\)

\(\frac{2^{19}\times27^3+15\times4^9\times9^4}{6^9\times2^{10}+12^{10}}\)

\(=\frac{2^{19}\times\left(3^3\right)^3+5\times3\times\left(2^2\right)^9\times\left(3^2\right)^4}{\left(2\times3\right)^9\times2^{10}+\left(3\times4\right)^{10}}\)

\(=\frac{2^{19}\times3^9+3\times5\times2^{18}\times3^8}{3^9\times2^9\times2^{10}+3^{10}\times4^{10}}\)

\(=\frac{2^{19}\times3^9+5\times2^{18}\times3^9}{3^9\times2^{19}+3^{10}\times\left(2^2\right)^{10}}\)

\(=\frac{2^{18}\times3^9\times\left(2+5\right)}{3^9\times2^{19}+3^{10}\times2^{20}}\)

\(=\frac{2^{18}\times3^9\times7}{2^{19}\times3^9\times\left(1+3\times2\right)}\)

\(=\frac{7}{2\times\left(1+6\right)}\)

\(=\frac{7}{2\times7}\)

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

 A = 2^19.27^3+15.4^9.9^4 / 6^9.2^10+12^10 
= 2^19.3^9 + 5.2^18.3^9 / 3^9.2^19 + 2^20.3^10 
= 2^18.3^9 ( 2 + 5 ) / 2^19.3^9.(1 + 2.3) 
= (2 + 5) / 2(1 + 6) 
= 7 / 2.7 
= 1/2

\(\frac{2^{19}.3^9+3^{13}.5.2^{18}}{2^{19}.3^9+2^{20}.3^{10}}=\frac{2^{18}\left(3^9+3^{13}.5\right)}{2^{19}\left(\cdot3^9+2.3^{10}\right)}=\frac{2^{18}.3^9\left(1+3^4.5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{1+3^4.5}{2.7}=\frac{406}{14}=29\)

A=2^19.3^9+3.5.2^18.3^8/3^9.2^9.2^10+3^10.2^20.

A=2^18.3^9.2+3^9.2^18.5/3^9.2^18.2+3^9.

A=3^9.2^18.(2+5)/3^9.2^18.(2+3.2^2).

A=7/14.

A=1/2.

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

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

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

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

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

\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.\left(3^3\right)^3+5.3.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)

\(=\frac{2^{19}.3^9+5.3.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^{19}.3^9+2^{20}.3^{10}}=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{2^{18}.3^9}{2^{19}.3^9}=\frac{1}{2}\)

P/s: Sai gì bỏ qua =)