(6^9 . 2^10 + 12^10) : (2^19 . 27^3 + 15.4^9 . 9^4)
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DT
0
NV
1
21 tháng 2 2023
\(B=\dfrac{2^{19}\cdot27^3+15.4^9\cdot9^4}{6^9+2^{10}\cdot3^{10}}\)
\(\Rightarrow B=\dfrac{2^{19}\cdot\left(3^3\right)^3+3\cdot5\cdot4^9\cdot\left(3^2\right)^4}{2^3\cdot3^3+\left(2\cdot3\right)^{10}}\)
\(\Rightarrow B=\dfrac{2^{19}\cdot3^9+3\cdot5\cdot4^9\cdot3^8}{\left(2\cdot3\right)^3+\left(2\cdot3\right)^{10}}\)
\(\Rightarrow B=\dfrac{2^{19}\cdot3^9+5\cdot\left(2^2\right)^9\cdot3^9}{\left(2\cdot3\right)^{13}}\)
\(\Rightarrow B=\dfrac{2^{19}\cdot3^9+5\cdot2^{18}\cdot3^9}{2^{13}\cdot3^{13}}\)
\(\Rightarrow B=\dfrac{2\cdot\left(2^{18}\cdot3^9\right)+5\cdot\left(2^{18}\cdot3^9\right)}{2^{13}\cdot3^{13}}\)
\(\Rightarrow B=\dfrac{\left(2^{18}\cdot3^9\right)\cdot\left(2+5\right)}{2^{13}\cdot3^{13}}\)
\(\Rightarrow B=\dfrac{2^{18}\cdot3^9\cdot7}{2^{13}\cdot3^{13}}=\dfrac{2^{13}\cdot2^5\cdot3^9\cdot7}{2^{13}\cdot3^9\cdot3^4}\)
\(\Rightarrow B=\dfrac{2^5\cdot7}{3^4}\)
IW
14 tháng 7 2016
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}.12^{10}}\)
\(=\frac{4^9.2.9^3.3^3+3.5.4^9.9^3.3^2}{6^9.2^{10}.2^{10}.6^{10}}\)
\(=\frac{4^9.9^3.3^2.6+4^9.9^3.3^2.15}{6^{19}.2^{20}}\)
\(=\frac{4^9.9^3.3^2.31}{2^{39}.3^{19}}\)
\(=\frac{4^9.3^6.31}{4^{19}.2.3^{17}}\)
\(=\frac{31}{4^{10}.3^{11}.2}\)
NM
2
XO
13 tháng 9 2020
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}=\frac{2^{19}.3^9+3^9.2^{18}.5}{2^{19}.3^9+3^{10}.2^{20}}\)
\(=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{7}{2.7}=\frac{1}{2}\)
13 tháng 9 2020
\(M=\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
\(=\frac{2^{19}\cdot\left(3^3\right)^3+3\cdot5\cdot\left(2^2\right)^9\cdot\left(3^2\right)^4}{6^9\cdot2^{10}+6^{10}\cdot2^{10}}\)
\(=\frac{2^{19}\cdot3^9+5\cdot2^{18}\cdot3\cdot3^8}{6^9\cdot2^{10}\left(6+1\right)}\)
\(=\frac{2^{19}\cdot3^9+5\cdot2^{18}\cdot3^9}{6^9\cdot2^{10}\cdot7}\)
\(=\frac{2^{18}\cdot3^9\left(2+5\right)}{2^{10}\cdot2^9\cdot3^9\cdot7}\)
\(=\frac{2^{18}\cdot3^9\cdot7}{2^{19}\cdot3^9\cdot7}\)
\(=\frac{1}{2}\)
TN
16 tháng 8 2015
\(\frac{3^2.4^2.2^{32}}{11.2^{13}.4^{11}-16^9}=\frac{3^2.2^4.2^{32}}{11.2^{13}.2^{22}-2^{36}}=\frac{3^2.2^{36}}{11.2^{35}-2^{36}}=\frac{3^2.2^{36}}{2^{35}.\left(11-2\right)}=\frac{9.2}{9}=2\)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{6^9.2^{10}+6^{10}.2^{10}}=\frac{2^{19}.3^9+3^9.5.2^{18}}{6^9.2^{10}.\left(1+6\right)}=\frac{2^{18}.3^9.\left(2+5\right)}{2^9.3^9.2^{10}.7}=\frac{2^{18}.7}{2^{19}.7}=\frac{1}{2}\)
LV
1
14 tháng 7 2017
Ta có:
\(\frac{2^{19}.27^9+15.4^9.9^4}{6^9.2^{12}+12^{10}}=\frac{2^{19}.\left(3^3\right)^9+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{12}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^{27}+3.5.2^{18}.3^8}{2^9.3^9.2^{12}+2^{20}.3^{10}}=\frac{2^{19}.3^{27}+3^9.2^{18}.5}{2^{21}.3^9+2^{20}.3^{10}}=\frac{2^{18}.3^9.\left(2.3^{18}+5\right)}{2^{20}.3^9.\left(2+3\right)}\)
\(=\frac{1.1.\left(2.3^{18}+5\right)}{2^2.1.5}=\frac{2.3^{18}+5}{20}\)
CX
0
(69. 210 + 1210) : (219 . 273 + 15. 49. 94)
= \(\frac{6^9.2^{10}+12^{10}}{2^{19}.27^3+15.4^9.9^4}=\frac{2^9.3^9.2^{10}+2^{20}.3^{10}}{2^{19}.3^9+3.5.2^{18}.3^8}=\frac{2^{19}.3^9\left(1+2.3\right)}{2^{18}.3^9\left(2+5\right)}=\frac{2.7}{7}=2\)
\(\left(6^9×2^{10}+12^{10}\right):\left(2^{19}×27^3+15×4^9×9^4\right)\)
\(=\frac{6^9×2^{10}+12^{10}}{2^{19}×27^3+15×4^9×9^4}\)
\(\frac{2^9×3^9×2^{10}+2^{10}×3^{10}}{2^{19}×3^9+3×5×2^{18}×2^8}\)
\(=\frac{2^{19}×3^9\left(1+2×3\right)}{2^{18}×3^9\left(2+5\right)}\)
\(=\frac{2×7}{7}\)
\(=2\)