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a: \(A=\dfrac{16^5\cdot15^5}{2^{10}\cdot3^5\cdot5^4}=\dfrac{2^{20}\cdot3^5\cdot5^5}{2^{10}\cdot3^5\cdot5^4}=2^{10}\cdot5=5120\)
b: \(B=\dfrac{2^{15}\cdot3+2^{19}\cdot10}{2^{12}\cdot26}=\dfrac{2^{15}\left(3+2^4\cdot10\right)}{2^{13}\cdot13}=2^2\cdot\dfrac{163}{13}=\dfrac{652}{13}\)
a) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{20}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...........\frac{19}{20}=\frac{1}{20}\)
b) \(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2012}}\)
=> \(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)
=> \(2A-A=\left(2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)
=> \(A=2-\frac{1}{2^{2012}}\)
c) \(\frac{7}{4}.\left(\frac{3333}{1212}+\frac{3333}{2020}+\frac{3333}{3030}+\frac{3333}{4242}\right)\)
\(=\frac{7}{4}\left(\frac{33}{12}+\frac{33}{20}+\frac{33}{30}+\frac{33}{42}\right)\)
\(=\frac{7}{4}.33\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(=\frac{231}{4}.\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(=\frac{231}{4}.\left(\frac{1}{3}-\frac{1}{7}\right)\)
\(=\frac{231}{4}.\frac{4}{21}=11\)
d.e) ktra lại đề
\(A=\dfrac{5}{11}.\dfrac{5}{7}+\dfrac{5}{11}.\dfrac{2}{7}+\dfrac{6}{11}=\dfrac{5}{11}\left(\dfrac{5}{7}+\dfrac{2}{7}\right)+\dfrac{6}{11}=\dfrac{5}{11}.1+\dfrac{6}{11}=\dfrac{5}{11}+\dfrac{6}{11}=\dfrac{11}{11}=1\)
\(B=\dfrac{3}{13}.\dfrac{6}{11}+\dfrac{3}{13}.\dfrac{9}{11}-\dfrac{3}{13}.\dfrac{4}{11}=\dfrac{3}{13}\left(\dfrac{6}{11}+\dfrac{9}{11}-\dfrac{4}{11}\right)=\dfrac{3}{13}.1=\dfrac{3}{13}\)
\(C=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{3}{6}-\dfrac{2}{6}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right).0=0\)
a) \(A=\left(\dfrac{3}{4}:\dfrac{2}{3}\right):\dfrac{3}{5}=\left(\dfrac{3}{4}\cdot\dfrac{3}{2}\right)\cdot\dfrac{5}{3}=\dfrac{9}{8}\cdot\dfrac{5}{3}=\dfrac{15}{8}\)
b) \(B=\dfrac{3}{4}:\left(\dfrac{2}{5}:\dfrac{3}{5}\right)=\dfrac{3}{4}:\left(\dfrac{2}{5}\cdot\dfrac{5}{3}\right)=\dfrac{3}{4}:\dfrac{2}{3}=\dfrac{3}{4}\cdot\dfrac{3}{2}=\dfrac{9}{8}\)
c) \(C=\left(\dfrac{11}{12}:\dfrac{33}{16}\right)\cdot\dfrac{3}{5}=\left(\dfrac{11}{12}\cdot\dfrac{16}{33}\right)\cdot\dfrac{3}{5}=\dfrac{4}{9}\cdot\dfrac{3}{5}=\dfrac{4}{15}\)
a.
A=\(\left(\dfrac{3}{4}:\dfrac{2}{3}\right):\dfrac{3}{5}\)
=\(\left(\dfrac{3}{4}.\dfrac{3}{2}\right):\dfrac{3}{5}\)
=\(\dfrac{9}{8}:\dfrac{3}{5}\)
=\(\dfrac{9}{8}.\dfrac{5}{3}=\dfrac{45}{24}=\dfrac{15}{8}\)
b.
B=\(\dfrac{3}{4}:\left(\dfrac{2}{5}:\dfrac{3}{5}\right)\)
=\(\dfrac{3}{4}:\left(\dfrac{2}{5}.\dfrac{5}{3}\right)\)
=\(\dfrac{3}{4}:\dfrac{2}{3}=\dfrac{3}{4}.\dfrac{3}{2}\)
=\(\dfrac{9}{8}\)
c.
C=\(\left(\dfrac{11}{12}:\dfrac{33}{16}\right).\dfrac{3}{5}\)
=\(\left(\dfrac{11}{12}.\dfrac{16}{33}\right).\dfrac{3}{5}\)
=\(\dfrac{4}{9}.\dfrac{3}{5}=\dfrac{12}{45}\)
=\(\dfrac{4}{15}\)