A= 4^5.9^4-2.6^9
2^10.3^8+6^8.20
B= 4^6.9^5+6^9.120
8^4.3^12-6^11
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L
0
24 tháng 5 2022
a: \(A=\dfrac{5^2\cdot3^{11}\cdot2^{11}\cdot2^8+3^2\cdot2^2\cdot2^{12}\cdot3^6\cdot3^2\cdot5^2}{2\cdot2^{12}\cdot3^{12}\cdot2^4\cdot5^4-3^8\cdot960^3}\)
\(=\dfrac{5^2\cdot3^{11}\cdot2^{19}+3^{10}\cdot2^{14}\cdot5^2}{2^{17}\cdot3^{12}\cdot5^4-3^{11}\cdot2^{18}\cdot5^3}\)
\(=\dfrac{5^2\cdot2^{14}\cdot3^{10}\left(3\cdot2^5+1\right)}{2^{17}\cdot3^{11}\cdot5^3\left(3\cdot5-2\right)}=\dfrac{1}{5}\cdot\dfrac{1}{8}\cdot\dfrac{1}{10}\cdot\dfrac{97}{13}=\dfrac{97}{5200}\)
b: \(B=\dfrac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=\dfrac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=\dfrac{2}{3}\cdot\dfrac{6}{5}=\dfrac{12}{15}=\dfrac{4}{5}\)
3 tháng 7 2018
a)\(\dfrac{2^{15}.3^8}{2^6.3^6.2^9}\)\(\dfrac{ }{ }\)=\(^{3^2}\)=9
b)\(\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.15}{-2^{12}.3^{12}-2^{11}.3^{11}}\)=\(\dfrac{2^{11}.3^{11}.\left(1+15\right)}{2^{11}.3^{11}\left(-2.3-1\right)}\)
=\(\dfrac{32}{-21}\)
c)\(\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)=\(\dfrac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}\)=\(-\dfrac{1}{3}\)
em dựa vào vd \(\dfrac{4^{16}}{2^8}\)= \(\dfrac{\left(2^2\right)^{16}}{2^8}=\dfrac{2^{16\cdot2}}{2^8}=2^4=16\)
21 tháng 6 2023
\(=\dfrac{-2^{12}\cdot3^{10}-2^{12}\cdot3^{10}\cdot5}{-2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot7}=\dfrac{2\cdot6}{3\cdot7}=\dfrac{12}{21}=\dfrac{4}{7}\)
L
4
S
5 tháng 1 2023
\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.5}\)
\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}=\dfrac{2.6}{3.5}=\dfrac{4}{5}\)
10 tháng 7 2016
\(4^6.9^5+6^9.120:8^4.3^{12}+6^{11}=\frac{4^6.9^5+6^9.120}{8^4.3^{12}+6^{11}}=\frac{ \left(2^2\right)^6.\left(3^2\right)^5+6^9.6.20}{2^3.3^{12}+6^9.6.6}=\frac{2^{12}.3^{10}+20}{2^3.3^{12}+6}=\frac{2^9+20}{3^2+6}\)
\(\frac{2^9+20}{3^2+6}=\frac{512+20}{9+6}=\frac{532}{15}\)
\(A=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}=\frac{2^{10}.3^8-2^{10}.3^8.3}{2^{10}.3^8+2^{10}.3^8.5}\)
\(=\frac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}=-\frac{2}{6}=-\frac{1}{3}\)
\(B=\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{11}.2.3^{10}.\left(1+5\right)}{2^{11}.3^{10}.3.\left(6-1\right)}=\frac{12}{15}=\frac{4}{5}\)
\(A=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\frac{2^{10}.3^8-2^2.3^9}{2^{10}.3^8-\left(-\left(2^2.3^8.5\right)\right)}=\frac{2^2.3^9}{-\left(2^2.3^8.5\right)}=-\frac{3}{5}\)