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\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}\)
\(=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^{19}.3^9+3^{10}.2^{20}}\)
\(=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+3.2\right)}\)
\(=\frac{7}{2.7}=\frac{1}{2}\)
\(=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{6^9.2^{10}+6^{10}.2^{10}}=\frac{2^{19}.3^9+3^9.5.2^{18}}{6^9.2^{10}.\left(1+6\right)}=\frac{2^{18}.3^9.\left(2+5\right)}{2^9.3^9.2^{10}}=\frac{2^{18}.7}{2^{19}.7}=\frac{1}{2}\)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.\left(3^3\right)^3+5.3.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^9+5.3.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^{19}.3^9+2^{20}.3^{10}}=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{2^{18}.3^9}{2^{19}.3^9}=\frac{1}{2}\)
P/s: Sai gì bỏ qua =)
Ta có :\(\frac{6^8.2^4-4^5.18^4}{27^3.8^4-3^9.2^{13}}=\frac{\left(2.3\right)^8.2^4-\left(2^2\right)^5.\left(3^2.2\right)^4}{\left(3^3\right)^3.\left(2^3\right)^4-3^9.2^{13}}=\frac{2^{12}.3^8-2^{14}.3^8}{3^9.2^{12}-3^9.2^{13}}=\frac{3^8.2^{12}.\left(2^2-1\right)}{3^9.2^{12}.\left(1-2\right)}\)
\(=\frac{3^9.2^{12}}{-3^9.2^{12}}=-1\)
\(\frac{6^8\cdot2^2-4^5\cdot18^4}{27^3\cdot8^4-3^9\cdot2^{13}}\)
\(=\frac{\left(2.3\right)^8.2^4-\left(2^2\right)^5.\left(3^2.2\right)^4}{\left(3^3\right)^3.\left(2^3\right)^4-3^9.2^{13}}\)
\(=\frac{2^{12}.3^8-2^{14}.3^8}{3^9.2^{12}-3^9.2^{14}}\)
\(=\frac{3^8.2^{12}.\left(2^2-1\right)}{3^9.2^{12}.\left(1-2\right)}\)
\(=\frac{3^9.2^{12}}{-3^9.2^{12}}=-1\)
\(C=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^9.3^9.2^{10}+3^{10}.2^{20}}\)
\(C=\frac{3^9.\left(2^{19}+5.2^{18}\right)}{3^9.\left(2^9.2^{10}+3.2^{20}\right)}\)
\(C=\frac{2^{19}+5.2^{18}}{2^9.2^{10}+3.2^{20}}\)suy ra \(C=\frac{2^{18}.\left(2+5\right)}{2^{18}.\left(2+3.2^2\right)}\)
\(C=\frac{7}{14}\)
Vậy \(C=\frac{1}{2}\)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(=\frac{2^{19}.3^9.\left(1+5\right)}{2^{19}.3^9.\left(1+2.3\right)}=\frac{6}{7}\)
\(=\frac{2^{19}.3^9+3^9.5.2^{18}}{2^9.3^9.2^{10}+2^{20}.3^{10}}=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{1}{2}\)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^4.2^{10}+12^{10}}=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^42^{10}+\left(2^2.3\right)^{10}}=\frac{2^{19}.3^9+2^{18}.3^9.5}{2^{14}.3^4+2^{20}.3^{10}}\)
\(=\frac{2^{14}.3^4\left(2^5.3^5+2^4.3^5.5\right)}{2^{14}.3^4\left(1+2^6.3^6\right)}=\frac{2^5.3^5+2^4.3^5.5}{1+2^6.3^6}=\frac{27216}{46657}\)
Có lẽ bạn gõ nhầm đề một chút. Mình sẽ làm theo đề sửa lại.
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^92^{10}+\left(2^2.3\right)^{10}}=\frac{2^{19}.3^9+2^{18}.3^9.5}{2^{19}.3^9+2^{20}.3^{10}}\)
\(=\frac{2^{18}.3^9\left(2+5\right)}{2^{18}.3^9\left(2+2^2.3\right)}=\frac{7}{14}=\frac{1}{2}\).