\(\dfrac{5}{2}-\dfrac{2}{11}\left(\dfrac{4}{3}+\dfrac{1}{2}\right)\)
\(=\dfrac{5}{2}-\dfrac{2}{11}\cdot\left(\dfrac{8}{6}+\dfrac{3}{6}\right)\)
\(=\dfrac{5}{2}-\dfrac{2}{11}\cdot\dfrac{11}{6}=\dfrac{5}{2}-\dfrac{1}{3}=\dfrac{15}{6}-\dfrac{2}{6}=\dfrac{13}{6}\)
\(\left(\dfrac{8}{27}\right)^{20}:\left(\dfrac{2}{3}\right)^{58}\)
\(=\left(\dfrac{2}{3}\right)^{60}:\left(\dfrac{2}{3}\right)^{58}\)
\(=\left(\dfrac{2}{3}\right)^{60-58}=\left(\dfrac{2}{3}\right)^2=\dfrac{4}{9}\)
\(2^2\cdot2^4=2^{2+4}=2^6;\left(2^2\right)^3=2^{2\cdot3}=2^6\)
Do đó: \(2^2\cdot2^4=\left(2^2\right)^3\)
\(\dfrac{5}{2}-\dfrac{2}{11}\left(\dfrac{4}{3}+\dfrac{1}{2}\right)\)
\(=\dfrac{5}{2}-\dfrac{2}{11}.\left(\dfrac{8}{6}+\dfrac{3}{6}\right)\)
\(=\dfrac{5}{2}-\dfrac{2}{11}.\dfrac{11}{6}\)
\(=\dfrac{5}{2}-\dfrac{1}{3}\)
\(=\dfrac{15}{6}-\dfrac{2}{6}\)
\(=\dfrac{13}{6}\)
\(---------\)
\(\left(\dfrac{8}{27}\right)^{20}:\left(\dfrac{2}{3}\right)^{58}=\left(\dfrac{2}{3}\right)^{60}:\left(\dfrac{2}{3}\right)^{58}=\left(\dfrac{2}{3}\right)^{60-58}=\left(\dfrac{2}{3}\right)^2=\dfrac{4}{9}\)
\(--------------\)
Ta có: \(2^2.2^4=2^{2+4}=2^6\)
\(\left(2^2\right)^3=\left(2\right)^{2.3}=2^6\)
Vì \(6=6\) nên \(2^6=2^6\)
hay \(2^2.2^4=\left(2^2\right)^3\)