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\(\frac{3\cdot11+1}{11}\cdot\frac{27\cdot46+27}{46}=\frac{34}{11}\cdot\frac{1269}{46}\)\(=\frac{21573}{253}\)
K mk nha thanks
\(=[3\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{81}+...+\frac{1}{2187}\right)-\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{81}+...+\frac{1}{2187}\right)]:2\)
\(=\left(1+\frac{1}{3}+\frac{1}{9}+...+\frac{1}{729}-\frac{1}{3}-\frac{1}{9}-\frac{1}{81}-...-\frac{1}{2187}\right):2\)
\(=\left(1-\frac{1}{2187}\right):2=\frac{2186}{2187}.\frac{1}{2}=\frac{1093}{2187}\)
a) \(\frac{3}{5}\times\frac{8}{27}\times\frac{5}{3}\)
\(=\left(\frac{3}{5}\times\frac{5}{3}\right)\times\frac{8}{27}\)
\(=1\times\frac{8}{27}\)
\(=\frac{8}{27}\)
b) \(\frac{7}{19}\times\frac{1}{3}+\frac{7}{19}\times\frac{2}{3}\)
\(=\frac{7}{19}\times\left(\frac{1}{3}+\frac{2}{3}\right)\)
\(=\frac{7}{19}\times1\)
\(=\frac{7}{19}\)
a=1 +1/3 +1/3^2 +1/3^3 +1/3^4 +1/3^5+1/3^6
3a=3 +1 +1/3 +1/3^2 + 1/3^3 +...+1/3^5
3a -a=[3 +1 +1/3 +1/3^2 +...+1/3^5] -1 -1/3 -1/3^2 -.........-1/3^6
2a =3- 1/3^6
a=[3-1/3^6] :2
a) \(11^{21}>9^{21}=\left(3^2\right)^{21}=3^{2.21}=3^{42}>3^{39}\)
b) \(5^{36}=\left(5^3\right)^{12}=125^{12}\)
\(11^{24}=\left(11^2\right)^{12}=121^{12}\)
Ta có: \(125>121\Rightarrow125^{12}>121^{12}\Rightarrow5^{36}>11^{24}\)
c) \(21^{15}=\left(3.7\right)^{15}=3^{15}.7^{15}\)
\(27^5.49^8=\left(3^3\right)^5.\left(7^2\right)^8=3^{15}.7^{16}\)
Ta có: \(7^{15}< 7^{16}\Rightarrow3^{15}.7^{15}< 3^{15}.7^{16}\Rightarrow2^{15}< 27^5.49^8\)
d) \(3^{99}=\left(3^3\right)^{33}=27^{33}>11^{21}\)
\(\frac{9}{16}:\frac{27}{8}=\frac{3^2:3^3}{2^4:2^3}=\frac{\frac{1}{3}}{2}=\frac{1}{6}\)
b tương tự nha
\(\frac{9}{16}:\frac{27}{8}=\frac{9}{16}\cdot\frac{8}{21}=\frac{3\cdot3\cdot4\cdot2}{8\cdot2\cdot7\cdot3}=\frac{14}{3}\)
\(\frac{40}{7}:\frac{5}{14}=\frac{40}{7}\cdot\frac{14}{5}=\frac{4\cdot5\cdot2\cdot7\cdot2}{7\cdot5}=\frac{16}{1}=16\)
Chúc bạn học tốt
Bài này bằng 3.(vì 3.3.3=27)
\(\sqrt[3]{27}=3\)