Tính (tính nhanh nếu có thể):
a) \(\dfrac{-13}{4}+\dfrac{19}{12}+\dfrac{5}{6}\)
b) \(\dfrac{7.6^{10}.2^{20}.3^6-2^{19}.6^{15}}{9.6^{19}.2^9-4.3^{17}.2^{26}}\)
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6 tháng 8 2020
Bài làm:
Ta có: \(\frac{7.6^{10}.2^{20}.3^6-2^{19}.6^{15}}{9.6^{19}.2^9-4.3^{17}.2^{26}}\)
\(=\frac{7.2^{10}.3^{10}.2^{20}.3^6-2^{19}.2^{15}.3^{15}}{3^2.2^{19}.3^{19}.2^9-2^2.3^{17}.2^{26}}\)
\(=\frac{2^{30}.3^{16}.7-2^{34}.3^{15}}{2^{28}.3^{21}-2^{28}.3^{17}}\)
\(=\frac{2^{30}.3^{15}\left(3.7-2^4\right)}{2^{28}.3^{17}\left(3^4-1\right)}\)
\(=\frac{2^2\left(21-16\right)}{3^2\left(81-1\right)}\)
\(=\frac{2^2.5}{3^2.80}\)
\(=\frac{1}{36}\)
18 tháng 2 2023
a: \(A=21\cdot100-11\cdot100+90\cdot100+100\cdot125\cdot16\)
\(=100\left(21-11+90\right)+100\cdot2000\)
\(=100\left(10+90+2000\right)=2100\cdot100=210000\)
b: \(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}=2\)
NT
2
21 tháng 5 2018
\(B=\frac{7.6^{10}.2^{20}.3^6-2^{19}.6^{15}}{9.6^{19}.2^9-4.3^{17}.2^{26}}\)
\(B=\frac{7.\left(2.3\right)^{10}.2^{20}.3^6-2^{19}.\left(2.3\right)^{15}}{3^2.\left(2.3\right)^{19}.2^9-2^2.3^{17}.2^{26}}\)
\(B=\frac{7.2^{30}.3^{16}-2^{34}.3^{15}}{3^{21}.2^{11}-2^{28}.3^{17}}\)
\(B=\frac{2^{30}.3^{15}.\left(7.3-2^4\right)}{3^{17}.2^{11}.\left(3^4-2^{17}\right)}\)
\(B=\frac{2^{19}.\left(21-2^4\right)}{3^2.\left(3^4-2^{17}\right)}\)
@_@ tự tính!
21 tháng 5 2018
\(B=\frac{7.\left(2.3\right)^{10}.2^{20}.3^6-2^{19}.\left(2.3\right)^{15}}{3^2.\left(2.3\right)^{19}.2^9-4.3^{17}.2^{26}}\\ B=\frac{7.2^{10}.3^{10}.2^{20}.3^6-2^{19}.2^{15}.3^{15}}{3^2.2^{19}.3^{19}.2^9-2^2.3^{17}.2^{26}}\\ B=\frac{7.2^{30}.3^{16}-2^{34}.3^{15}}{3^{21}.2^{28}-2^{28}.3^{17}}\)
\(B=\frac{7.2^{30}.3.3^{15}-2^{34}.3^{15}}{3^{15}.3^6.2^{28}-2^{28}.3^{15}.3^2}\\ B=\frac{3^{15}.\left(7.2^{30}.3-3^{34}\right)}{3^{15}.\cdot\left(3^6-3^2\right)}\\ B=\frac{7.2^{30}.3-3^{34}}{3^6-3^2}\)
24 tháng 3 2023
a: \(=\dfrac{8}{9}\cdot\dfrac{9}{4}\cdot\dfrac{12}{19}\cdot\dfrac{19}{24}=\dfrac{1}{2}\cdot2=1\)
b: \(=\dfrac{5}{16}\cdot\dfrac{17}{15}\cdot\dfrac{8}{17}=\dfrac{5}{16}\cdot\dfrac{8}{15}=\dfrac{40}{240}=\dfrac{1}{6}\)
c: \(=\dfrac{4}{13}\left(\dfrac{2}{7}+\dfrac{5}{7}\right)-\dfrac{3}{26}=\dfrac{4}{13}-\dfrac{3}{26}=\dfrac{5}{26}\)
c: \(=\dfrac{3}{4}\left(\dfrac{6}{11}+\dfrac{5}{11}\right)-\dfrac{1}{5}=\dfrac{3}{4}-\dfrac{1}{5}=\dfrac{11}{20}\)
31 tháng 12 2022
a)= 2021.2021-2020.(2021+1)
= 2021.(2020+1)-2020.(2021+1)
= (2021.2020)+2021-(2020.2021)-2020
= 1
31 tháng 12 2022
b) B= (1+2-3-4)+(5+6-7-8)+(9+10-11-12)...........+(2017+2018-2019-2020)+2021
B= -4+(-4)+....................(-4)+2021
B= -4x505+2021
B= -2020 + 2021
B = 1
HV
2
1 tháng 5 2015
\(=\frac{7.6^{11}.2^{19}.3^5-2^{19}.6^{15}}{3^{21}.2^{28}-3^{17}.2^{28}}=\frac{2^{19}.6^{11}.\left(7.3^5-6^4\right)}{3^{17}.2^{28}.\left(3^4-1\right)}=\frac{2^{30}.3^{11}.3^4.\left(7.3-2^4\right)}{3^{17}.2^{28}.\left(3^4-1\right)}=\frac{2^2.13}{3^2.80}=\frac{13}{9.20}=\frac{13}{180}\)
2
7 tháng 2 2023
`6/7 . 8/13 +6/7 . 9/13+3/13 . 6/7`
`=6/7 . (8/13+9/13+3/13)`
`=6/7 . 20/13`
`=120/91`
VN
7 tháng 2 2023
\(\dfrac{6}{7}.\dfrac{8}{13}+\dfrac{6}{7}.\dfrac{9}{13}+\dfrac{3}{13}.\dfrac{6}{7}\)
\(=\dfrac{6}{7}.\left(\dfrac{8}{13}+\dfrac{9}{13}+\dfrac{3}{13}\right)\)
\(=\dfrac{6}{7}.\left(\dfrac{8+9+3}{13}\right)\)
\(=\dfrac{6}{7}.\dfrac{20}{13}\)
\(=\dfrac{6.20}{7.13}\)
\(=\dfrac{120}{91}\)
a: \(=\dfrac{-39+19+10}{12}=\dfrac{-10}{12}=\dfrac{-5}{6}\)
b: \(=\dfrac{2^{30}\cdot3^{16}\cdot7-2^{34}\cdot3^{15}}{2^{28}\cdot3^{21}-2^{28}\cdot3^{17}}\)
\(=\dfrac{2^{30}\cdot3^{15}\left(3\cdot7-2^4\right)}{2^{28}\cdot3^{17}\left(3^4-1\right)}=\dfrac{2^2}{3^2}\cdot\dfrac{21-16}{80}=\dfrac{4}{9}\cdot\dfrac{5}{80}\)
\(=\dfrac{20}{720}=\dfrac{1}{36}\)