Rút gọn \(\frac{16.3^{11+4.27^4}}{^{9^7}}\)
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NN
0
LV
1
TN
0
Q
8 tháng 10 2016
\(A=\frac{2\cdot\left(2^3\right)^4\cdot\left(3^3\right)^8+2^2\cdot\left(2\cdot3\right)^9}{2^7\cdot6^7+2^7\cdot\left(2^3\cdot5\right).\left(3^2\right)^4}\)
\(A=\frac{2\cdot2^{12}\cdot3^{24}+2^2\cdot\left(2\cdot3\right)^9}{12^7+2^7\cdot\left(2^3\cdot5\right)\cdot3^8}\)
Đến đó thì bí
HL
2
AK
10 tháng 4 2018
\(M=\frac{9^4.27^5.3^6.3^4}{3^8.81^4.243.8^2}\)
\(M=\frac{\left(3^2\right)^4.\left(3^3\right)^5.3^6.3^4}{3^8.\left(3^4\right)^4.\left(3^5\right).\left(2^3\right)}\)
\(M=\frac{3^8.3^{15}.3^6.3^4}{3^8.3^{16}.3^5.8}\)
\(M=\frac{3^{33}}{3^{29}.8}\)
\(M=\frac{3^4}{1.8}\)
\(M=\frac{81}{8}\)
Chúc bạn học tốt !!!
6 tháng 11 2017
a, \(\dfrac{2\cdot8^4\cdot27^2+4\cdot6^9}{2^7\cdot6^7+2^7\cdot40\cdot9^4}\)
=\(\dfrac{2\cdot\left(2^3\right)^4\cdot\left(3^3\right)^2+2^2\cdot2^9\cdot3^9}{2^7\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot\left(3^2\right)^4}\)
=\(\dfrac{2\cdot2^{12}\cdot3^6+2^{11}\cdot3^9}{2^{14}\cdot3^7+2^{10}\cdot5\cdot3^8}\)
=\(\dfrac{2^{11}\cdot3^6\cdot\left(2^2+3^3\right)}{2^{10}\cdot3^7\cdot\left(2^4+5\cdot3\right)}\)
=\(\dfrac{2^{11}\cdot3^6\cdot31}{2^{10}\cdot3^7\cdot31}\)
=\(\dfrac{2}{3}\)
6 tháng 11 2017
b, \(\dfrac{\dfrac{8}{27}\cdot\dfrac{9}{16}\cdot\left(-1\right)}{\dfrac{4}{25}\cdot\dfrac{-125}{1728}}\)
=\(\dfrac{\dfrac{8\cdot9\cdot\left(-1\right)}{27\cdot16}}{\dfrac{4\cdot\left(-125\right)}{25\cdot1728}}\)
=\(\dfrac{\dfrac{-1}{6}}{\dfrac{-5}{432}}\)
=\(\dfrac{-1}{6}\cdot\dfrac{-432}{5}\)
=\(\dfrac{72}{5}\)
AK
14 tháng 5 2018
\(\frac{15.3^{11}+4.27^4}{9^7}\)
\(=\frac{5.3.3^{11}+4.\left(3^3\right)^4}{\left(3^2\right)^7}\)
\(=\frac{5.3^{12}+4.3^{12}}{3^{14}}\)
\(=\frac{3^{12}.\left(5+4\right)}{3^{14}}\)
\(=\frac{3^{12}.9}{3^{14}}\)
\(=\frac{3^{12}.3^2}{3^{14}}\)
\(=\frac{3^{14}}{3^{14}}\)
\(=1\)
Chúc bạn học tốt !!!
14 tháng 5 2018
\(A=\frac{15.3^{11}+4.27^4}{9^7}\)
\(\Rightarrow\frac{3.5.3^{11}+4.3^{3.4}}{3^{2.7}}\)
\(\Rightarrow\frac{3^{12}.5+3^{12}.4}{3^{14}}\)
\(\Rightarrow\frac{3^{12}\left(5+4\right)}{3^{14}}\)
\(\Rightarrow\frac{9}{3^2}=\frac{9}{9}=1\)
Vậy ....
\(\frac{16.3^{11+4.27^4}}{9^7}=\frac{2^4.3^{11+2^2.3^{12}}}{3^{14}}\)
\(=\frac{2^4.3^{11+2^2.531441}}{3^{14}}=\frac{2^4.3^{2125764}}{3^{14}}=2^4.3^{2125750}\)
Ta có:
\(\frac{16.3^{11+4.27^4}}{9^7}=\frac{2^4.3^{11+2^2.\left(3^3\right)^4}}{\left(3^2\right)^7}=\frac{2^4.3^{11+2^2.3^{12}}}{3^{14}}=\frac{2^4.3^{11}.3^{2^2.3^{12}}}{3^{14}}=\frac{2^4.3^{15}.3^{3^{12}}}{3^{14}}=2^4.3^{3^{12}}\)
Vậy ...