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2 tháng 7 2019
a)\(\frac{11^4.6-11^5}{11^4-11^5}:\frac{9^8.3-9^9}{9^8.5+9^8.7}\)
\(=1.6:\frac{9^8.3-9^8.9}{9^8.\left(5+7\right)}\)
\(=6:\frac{9^8.\left(3-9\right)}{9^8.12}\)
\(=6:\frac{9^8.\left(-6\right)}{9^8.12}\)
\(=6:\left(-\frac{6}{12}\right)\)
\(=6:\left(-\frac{1}{2}\right)\)
\(=-12\)
b) 3/5 : ( -1/5-1/6)+3/5:(-1/3-16/15) ( mình chuyển về ps luôn )
=3/5: (-11/30) + 3/5 : (-7/5)
=3/5:[-11/30+(-7/5)]
=3/5:53/30
=18/53
c) (1/2-13/14):5/7-(-2/21+1/7):5/7
= -3/7:5/7-1/21:5/7
=(-3/7-1/21):5/7
=-10/21:5/7
=-2/3
câu b vá c mình làm tắt nha. chúc bạn học tốt
PA
9 tháng 7 2016
a.
\(\frac{11^4\times6-11^5}{11^4-11^5}=\frac{11^4\times\left(6-11\right)}{11^4\times\left(1-11\right)}=\frac{-5}{-10}=\frac{1}{2}\)
b.
\(\frac{9^8\times3-3^{18}}{9^8\times5+9^8\times7}=\frac{9^8\times3-\left(3^2\right)^9}{9^8\times\left(5+7\right)}=\frac{9^8\times3-9^9}{9^8\times12}=\frac{9^8\times\left(3-9\right)}{9^8\times12}=-\frac{6}{12}=-\frac{1}{2}\)
c.
\(\frac{10^5-10^5\times3}{10^5\times11}=\frac{10^5\times\left(1-3\right)}{10^5\times11}=-\frac{2}{11}\)
Chúc bạn học tốt
7 tháng 3 2018
\(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\frac{3^2.5^{20}.3^{27}-3.3^{30}.5^{18}}{7.3^{29}.5^{18}-3^{10}.3^{19}.5^{19}}\)
\(=\frac{3^{29}.5^{18}.5^2-3^2.3^{29}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{18}.5}\)
\(=\frac{3^{29}.5^{18}.\left(5^2-3^2\right)}{3^{29}.5^{18}.\left(7-5\right)}\)
\(=\frac{25-9}{2}\)
\(=\frac{16}{2}=8\)
UC
2
NV
31 tháng 5 2018
( mk sửa đề 1 chút nha )
\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
= \(\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
= \(\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
= \(\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}\)
= \(\frac{2.1}{1}\)
= 2
Hok tốt
( nhớ ủng hộ mk nha )
29 tháng 4 2019
Ta có: \(A=\frac{1}{3}-\frac{3}{4}+\frac{3}{5}+\frac{1}{73}-\frac{1}{36}+\frac{1}{15}-\frac{2}{9}\)
\(A=\left(\frac{1}{3}-\frac{2}{9}\right)+\left(\frac{3}{5}+\frac{1}{15}\right)-\frac{3}{4}-\frac{1}{36}+\frac{1}{73}\)
\(A=\left(\frac{3}{9}-\frac{2}{9}\right)+\left(\frac{9}{15}+\frac{1}{15}\right)-\left(\frac{3}{4}+\frac{1}{36}\right)+\frac{1}{73}\)
\(A=\frac{1}{9}+\frac{10}{15}-\frac{7}{9}+\frac{1}{73}\)
\(A=\frac{1}{9}+\frac{2}{3}-\frac{7}{9}+\frac{1}{73}\)
\(A=\frac{1}{9}+\frac{6}{9}-\frac{7}{9}+\frac{1}{73}\)
\(A=\frac{7}{9}-\frac{7}{9}+\frac{1}{73}\)
\(A=\frac{1}{73}\)
Vậy: \(A=\frac{1}{73}\)
14 tháng 10 2018
\(a)\)\(M=\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{399}{400}\)
\(M=\frac{4-1}{4}+\frac{9-1}{9}+\frac{16-1}{16}+...+\frac{400-1}{400}\)
\(M=1-\frac{1}{4}+1-\frac{1}{9}+1-\frac{1}{16}+...+1-\frac{1}{400}\)
\(M=\left(1+1+1+...+1\right)-\left(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{400}\right)\)
\(M=\left(1+1+1+...+1\right)-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{20^2}\right)\)
Do từ 2 đến 20 có \(20-2+1=19\) nên :
\(M=19-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{20^2}\right)\)
Đặt \(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{20^2}\)
\(A>\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{20.21}\)
\(A>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{20}-\frac{1}{21}\)
\(A>\frac{1}{2}-\frac{1}{21}\)
\(\Rightarrow\)\(M=19-A>19-\frac{1}{2}+\frac{1}{21}=18,5+\frac{1}{21}>8\)
\(\Rightarrow\)\(M>8\) ( đpcm )
Còn câu b) bn xem lại đề đi, nếu đề đúng thì mk sai :v
Chúc bạn học tốt ~
21 tháng 1 2019
\(M=\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+\frac{24}{25}...+\frac{399}{400}\)
\(=\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{9}\right)+\left(1-\frac{1}{16}\right)+\left(1-\frac{1}{25}\right)+...+\left(1-\frac{1}{400}\right)\)
\(=\left(1+1+1+....+1\right)-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{20^2}\right)\)
\(=19-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{20^2}\right)\)
Đặt \(N=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{20^2}\)
\(< P=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+....+\frac{1}{20\cdot21}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{20}-\frac{1}{21}\)
\(=\frac{1}{2}-\frac{1}{21}\)
\(\Rightarrow M+N>19-\frac{1}{2}+\frac{1}{21}=\frac{37}{2}+\frac{1}{21}>8\)
b sai đề.chừng nào chữa đề thì làm
\(\frac{3^8.5^9+15^8.3^2}{15^9.3^3-3^8.5^9}\)
\(=\frac{3^8.5^9+5^8.3^{10}}{5^9.3^{12}-3^8.5^9}\)
\(=\frac{3^8.5^8.\left(5+3^2\right)}{5^9.3^8.\left(3^4-1\right)}=\frac{14}{80}=\frac{7}{40}\)
\(=\frac{15^8.5+15^8.3^2}{15^8.5.3.3^3-15^8.5}\)
\(=\frac{15^8\left(5+9\right)}{15^8\left(5.3^4-5\right)}\)
\(=\frac{15^8.14}{15^8.400}\)
\(=\frac{14}{400}\)
\(=\frac{7}{200}\)