Tính giá trị biểu thức sau:
\(\frac{2^{20}.27^3+30.4^9.9^4}{6^9.4^5+12^{10}}\)
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CC
1
MM
2
DH
17 tháng 7 2017
\(\dfrac{2^{20}.27^3+30.4^9.9^4}{6^9.4^5+12^{10}}=\dfrac{2^{20}.3^9+3.2.5.2^{18}.3^8}{2^9.3^9+2^{10}+2^{20}.3^{10}}\)
\(=\dfrac{2^{19}.3^9.\left(2+5\right)}{2^9.3^9.\left(1+2^{11}.3\right)+2^{10}}=\dfrac{2^{10}.\left(2+5\right)}{1+2^{10}.\left(2.3+1\right)}\)
\(=\dfrac{2^{10}.7}{2^{10}.7+1}=\dfrac{7168}{7169}\)
Chúc bạn học tốt!!!
16 tháng 7 2017
\(\dfrac{2^{20}.27^3+30.4^9.9^4}{6^9.4^5+12^{10}}=\dfrac{2^{20}.3^9+2.3.5.2^{18}.3^8}{2^9.3^9+2^{20}.3^{10}}=\dfrac{2^{20}.3^9+5.2^{19}.3^9}{2^9.3^9+2^{20}.3^{10}}=\dfrac{2^9.3^9\left(2^{11}+5.2^{10}\right)}{2^9.3^9\left(1+2^{11}.3\right)}\)
\(\dfrac{2^{11}+5.2^{10}}{1+2^{11}.3}\)
tới bc này chiu :))
MM
1
16 tháng 7 2017
\(\dfrac{2^{20}\cdot27^3+30\cdot4^9\cdot9^4}{6^9\cdot4^5+12^{10}}\\ =\dfrac{2^{20}\cdot\left(3^3\right)^3+\left(2\cdot3\cdot5\right)\cdot\left(2^2\right)^9\cdot\left(3^2\right)^4}{\left(2\cdot3\right)^9\cdot\left(2^2\right)^5+\left(3\cdot4\right)^{10}}\\ =\dfrac{2^{20}\cdot3^9+2\cdot3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+3^{10}\cdot4^{10}}\\ =\dfrac{2^{20}\cdot3^9+2^{19}\cdot3^9\cdot5}{2^{19}\cdot3^9+3^{10}\cdot2^{20}}\\ =\dfrac{2^{19}\cdot3^9\left(2+5\right)}{2^{19}\cdot3^9\left(1+2\cdot3\right)}\\ =\dfrac{2^{19}\cdot3^9\cdot7}{2^{19}\cdot3^9\cdot7}\\ =1\)
16 tháng 9 2016
\(H=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(H=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(H=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(H=\frac{2^{19}.3^9+2^{18}.5.3^9}{2^{19}.3^9+2^{20}.3^{10}}\)
\(H=\frac{2^{18}.3^9.\left(2+5\right)}{2^{19}.3^9.\left(1+2.3\right)}\)
\(H=\frac{2^{18}.3^9.7}{2^{19}.3^9.\left(1+6\right)}\)
\(H=\frac{2^{18}.3^9.7}{2^{19}.3^9.7}=\frac{1}{2}\)
\(K=\frac{4^7.2^8}{3.2^{15}.16^2-5.2^2.\left(2^{10}\right)^2}\)
\(K=\frac{\left(2^2\right)^7.2^8}{3.2^{15}.\left(2^4\right)^2-5.2^2.2^{20}}\)
\(K=\frac{2^{14}.2^8}{3.2^{15}.2^8-5.2^{22}}\)
\(K=\frac{2^{22}}{3.2^{23}-5.2^{22}}\)
\(K=\frac{2^{22}}{2^{22}.\left(3.2-5\right)}=\frac{2^{22}}{2^{22}.1}=1\)
LP
1
12 tháng 2 2017
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}\)
\(=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^{19}.3^9+3^{10}.2^{20}}\)
\(=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+3.2\right)}\)
\(=\frac{7}{2.7}=\frac{1}{2}\)
NT
2
19 tháng 1 2017
Bạn đăng lên H.vn thử xem . Trên đấy có nhiều người trả lời giúp hơn đấy mà còn nhanh hơn nữa.
10 tháng 4 2022
\(P=\dfrac{2^{20}\cdot3^{10}+2^9\cdot2^{12}\cdot3^9}{15\cdot2^{18}\cdot3^8-2^{19}\cdot3^9}=\dfrac{2^{20}\cdot3^9\left(3+2\right)}{2^{18}\cdot3^9\cdot5-2^{19}\cdot3^9}\)
\(=\dfrac{2^{20}\cdot3^9\cdot5}{2^{18}\cdot3^9\left(5-2\right)}=4\cdot\dfrac{5}{3}=\dfrac{20}{3}\)
Ta có:
\(\frac{2^{20}\cdot27^3+30\cdot4^9\cdot9^4}{6^9\cdot4^5+12^{10}}=\frac{2^{20}\cdot\left[3^3\right]^3+2\cdot3\cdot5\cdot\left[2^2\right]^9\cdot\left[3^2\right]^4}{2^9\cdot3^9\cdot\left[2^2\right]^5+3^{10}\cdot\left[2^2\right]^{10}}=\frac{2^{20}\cdot3^{3\cdot3}+2\cdot3\cdot5\cdot2^{2\cdot9}\cdot3^{2\cdot4}}{2^9\cdot3^9\cdot2^{2\cdot5}+3^{10}\cdot2^{2\cdot10}}\)
\(=\frac{2^{20}\cdot3^9+2\cdot3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+3^{10}\cdot2^{20}}=\frac{2^{20}\cdot3^9+2^{19}\cdot3^9\cdot5}{2^{19}\cdot3^9+3^{10}\cdot2^{20}}=\frac{2^{19}\cdot3^9\left[2+5\right]}{2^{19}\cdot3^9\left[1+3\cdot2\right]}=\frac{2+5}{1+6}=\frac{7}{7}=1\)