Rút gọn biểu thức \(\frac{2^{19}.27^{3^{ }}+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
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P
2
18 tháng 5 2016
\(A=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(A=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(A=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(A=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^{19}.3^9+2^{20}.3^{10}}\)
\(A=\frac{2^{18}.3^9.\left(2+5\right)}{2^{18}.3^9.\left(2+2^2.3\right)}\)
\(A=1.\frac{2+5}{2+4.3}\)
\(A=\frac{7}{14}=\frac{1}{2}\)
Vậy \(A=\frac{1}{2}\)
SH
2
S
30 tháng 9 2016
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(=\frac{2^{19}.3^9.\left(1+5\right)}{2^{19}.3^9.\left(1+2.3\right)}=\frac{6}{7}\)
DT
1
16 tháng 7 2016
\(=\frac{2^{19}.3^9+3^9.5.2^{18}}{2^9.3^9.2^{10}+2^{20}.3^{10}}=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{1}{2}\)
SH
1
AH
7 tháng 10 2016
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
= \(\frac{2^{19}.3^9+5.2^{18}.3^9}{6^9.2^{10}+2^{10}.6^{10}}\)
=\(\frac{\left(2^{18}.3^9\right)\left(2+5\right)}{\left(6^9.2^{10}\right)\left(1+6\right)}\)
=\(\frac{7\left(2^{18}.3^9\right)}{7\left(3^9.2^9.2^{10}\right)}\)
= \(\frac{7\left(2^{18}.3^9\right)}{7\left(3^9.2^{19}\right)}\)
= \(\frac{1}{2}\)
NL
1
3 tháng 2 2022
\(=\dfrac{2^{19}\cdot3^9+2^{18}\cdot3^9\cdot5}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}=\dfrac{2^{18}\cdot3^9\cdot\left(2+5\right)}{2^{19}\cdot3^9\cdot7}=\dfrac{1}{2}\)
TM
1
2 tháng 2 2017
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^{10}.6^9+2^{10}.6^{10}}=\frac{2^{18}.3^9.\left(2+5\right)}{2^{10}.6^9\left(1+6\right)}=\frac{2^{18}.3^9.7}{2^{10}.6^9.7}=2^8.\left(\frac{1}{2}\right)^9=2^8.\frac{9}{2^9}=\frac{1}{2}.9=\frac{9}{2}\)Vậy C=\(\frac{9}{2}\)
LV
1
14 tháng 7 2017
Ta có:
\(\frac{2^{19}.27^9+15.4^9.9^4}{6^9.2^{12}+12^{10}}=\frac{2^{19}.\left(3^3\right)^9+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{12}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^{27}+3.5.2^{18}.3^8}{2^9.3^9.2^{12}+2^{20}.3^{10}}=\frac{2^{19}.3^{27}+3^9.2^{18}.5}{2^{21}.3^9+2^{20}.3^{10}}=\frac{2^{18}.3^9.\left(2.3^{18}+5\right)}{2^{20}.3^9.\left(2+3\right)}\)
\(=\frac{1.1.\left(2.3^{18}+5\right)}{2^2.1.5}=\frac{2.3^{18}+5}{20}\)
23 tháng 9 2016
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(=\frac{2^{19}.3^9+2^{19}.3^9.5}{2^{19}.3^9+2^{20}.3^{10}}\)
\(=\frac{2^{19}.3^9.\left(1+5\right)}{2^{19}.3^9\left(1+2.3\right)}\)
\(=\frac{6}{7}\)
6 tháng 8 2017
may mà m đăng để t đỡ phải viết (mỏi tay) Nguyen Ngoc Linh
6 tháng 8 2017
\(A=\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+2^{12}}\)
\(=\dfrac{2^{19}.3^9+5.2^{18}.3^9}{2^9.3^{19}+2^{12}}=\dfrac{2^{10}+5.2^8}{3^{10}+2^3}=\dfrac{2^7+5.2^5}{3^{10}}\)
LP
1
12 tháng 2 2017
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}\)
\(=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^{19}.3^9+3^{10}.2^{20}}\)
\(=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+3.2\right)}\)
\(=\frac{7}{2.7}=\frac{1}{2}\)
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