\(B=\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\) ZZUPS NHANH NHA
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46.95 + 69.120 / 84.312 - 611
= 212.315 + 212.310.5 / 212.312 - 211.311
= 212. 310.( 35 + 5 ) / 211.311( 2.3 - 1 )
= 2 . 248 / 3 . 5 = 496/15
\(=\frac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot5\cdot3}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=\frac{2^{12}\cdot3^{10}\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}\)\(=\frac{2^{13}\cdot3^{11}}{2^{11}\cdot3^{11}\cdot5}=\frac{4}{5}\)
\(B=\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(B=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(B=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(B=\frac{2^{11}.3^{10}.\left(2+2.5\right)}{2^{11}.3^{10}.\left(2.3^2-3\right)}\)
\(B=\frac{2+2.5}{2.3^2-3}\)
\(B=\frac{4}{5}\)
\(A=\frac{9^4.27^5.3^6.3^4}{3^8.814.234.8^2}=\frac{\left(3^2\right)^4.\left(3^3\right)^5.3^{10}}{3^8.2.407.2.3^2.13.\left(2^3\right)^2}=\frac{3^8.3^{15}.3^{10}}{2^8.3^{10}.13.407}=\frac{3^{23}}{2^8.13.407}\)
\(B=\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}=\frac{2^{12}.3^{10}+2^9.2^3.3^9.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.5}\)
=\(\frac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}=\frac{2^{13}.3^{11}}{2^{11}.3^{11}.5}=\frac{2^2}{5}=\frac{4}{5}\)