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13 tháng 6 2022
\(=\dfrac{\left[\dfrac{2^{13}\cdot3^{14}}{3^{13}}+\dfrac{3^{18}}{2^{12}}:\dfrac{3^{12}}{2^{24}}\right]}{2^{12}\cdot3^4+2^{12}\cdot3^2}\)
\(=\dfrac{\left[\dfrac{2^{13}}{3}+\dfrac{2^{12}}{3^6}\right]}{2^{12}\cdot3^2\cdot\left(3^2+1\right)}=\dfrac{2^{12}\cdot\left(\dfrac{2}{3}+\dfrac{1}{3^6}\right)}{2^{12}\cdot3^2\cdot10}\)
\(=\left(\dfrac{487}{729}\right):\dfrac{1}{90}=\dfrac{4870}{81}\)
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0
DH
25 tháng 6 2017
a, \(\dfrac{4^2.4^3}{2^{10}}=\dfrac{4^5}{2^{10}}=\dfrac{\left(2^2\right)^5}{2^{10}}=\dfrac{2^{10}}{2^{10}}=1\)
b, \(\dfrac{2^7.9^3}{6^5.8^2}=\dfrac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\dfrac{2^7.3^6}{2^5.3^5.2^6}=\dfrac{3}{2^4}=\dfrac{3}{16}\)
c, \(\dfrac{9^7.5^6.125^9}{15^{15}.5^{18}}=\dfrac{3^{21}.5^6.5^{27}}{5^{15}.3^{15}.5^{18}}=\dfrac{3^{21}.5^{33}}{3^{15}.5^{33}}=3^6=729\)
d, \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^9.\left(1+3.5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\dfrac{2.16}{3^2.5}=\dfrac{32}{45}\)
Chúc bạn học tốt!!!
10 tháng 9 2018
2
a) (2x - 1)4 = 81
<=> \(\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}}\)
P
0
`#3107.101107`
\(\dfrac{4^{10}\cdot9^6+3^{12}\cdot8^5}{6^{13}\cdot4-2^{16}\cdot3^{12}}\)
\(=\dfrac{2^{20}\cdot3^{12}+3^{12}\cdot2^{15}}{2^{13}\cdot3^{13}\cdot2^2-2^{16}\cdot3^{12}}\)
\(=\dfrac{3^{12}\cdot\left(2^{20}+2^{15}\right)}{3^{12}\cdot\left(2^{15}\cdot3-2^{16}\right)}\)
\(=\dfrac{2^{20}+2^{15}}{2^{15}\cdot3-2^{16}}\)
\(=\dfrac{2^{15}\cdot\left(2^5+1\right)}{2^{15}\cdot\left(3-2\right)}\)
\(=\dfrac{32+1}{1}\)
\(=33\)