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\(B=\dfrac{6^{30}\cdot3^{11}\cdot7-2^{31}\cdot5\cdot3^{40}}{2^{28}\cdot17\cdot3^{38}-6^{27}\cdot3^{11}}\)
\(=\dfrac{2^{30}\cdot3^{41}\cdot7-2^{31}\cdot5\cdot3^{40}}{2^{28}\cdot17\cdot3^{38}-2^{27}\cdot3^{38}}\)
\(=\dfrac{2^{30}\cdot3^{40}\left(3\cdot7-2\cdot5\right)}{2^{27}\cdot3^{38}\left(2\cdot17-1\right)}\)
\(=\dfrac{2^3\cdot3^2\cdot\left(21-10\right)}{34-1}=\dfrac{2^3\cdot3^2\cdot11}{33}=\dfrac{2^3\cdot3^2}{3}=2^3\cdot3=24\)
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\(A=2^2+2^2+2^3+...+2^{2021}\\ 2A=2^3+2^3+2^4+...+2^{2022}\\ A=2^{2022}+2^3-2^2-2^2\)
\(2A=8+2^3+...+2^{2022}\)
\(\Leftrightarrow A=2^{2022}+8-4-2^2=2^{2022}\)
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a, = 2^30.3^30.3^11.7-2^31.5.3^40
= 2^30.3^41.7-2^31.5.3^40
= 2^30.3^40.(3.7-2.5) = 2^30.3^40.11
b, = 2^28.17.3^38-2^27.3^27.3^11
= 2^28.17.3^38-2^27.3^38
= 2^27.3^38.(2.17-1) = 2^27.3^38.33
k mk nha
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