\(\left(\dfrac{-2}{3}\right)^3:\left(\dfrac{-2}{3}\right)^2+\dfrac{2^{40}\cdot3^{29}}{8^{13}\cdot9^{15}}\)

\(=\dfrac{-2}{3}+\dfrac{2^{40}\cdot3^{29}}{\left(2^3\right)^{13}\cdot\left(3^2\right)^{15}}\)

\(=\dfrac{-2}{3}+\dfrac{2^{40}\cdot3^{29}}{2^{39}\cdot3^{30}}\)

\(=\dfrac{-2}{3}+\dfrac{2}{3}\)

\(=0\)

\(Toru\)

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uk

\(\dfrac{3}{4}\cdot26\dfrac{2}{9}-38\dfrac{2}{9}\cdot\dfrac{3}{4}\)

\(=\dfrac{3}{4}\cdot\left(26\dfrac{2}{9}-38\dfrac{2}{9}\right)\)

\(=\dfrac{3}{4}\cdot\left(26+\dfrac{2}{9}-38-\dfrac{2}{9}\right)\)

\(=\dfrac{3}{4}\cdot-12\)

\(=3\cdot-3\)

\(=-9\)

\(\dfrac{3}{4}\cdot26\dfrac{2}{9}-38\dfrac{2}{9}\cdot\dfrac{3}{4}\)

\(=\dfrac{3}{4}\left(26\dfrac{2}{9}-38\dfrac{2}{9}\right)\)

\(=\dfrac{3}{4}\left[\left(26-38\right)+\left(\dfrac{2}{9}-\dfrac{2}{9}\right)\right]\)

\(=\dfrac{3}{4}\cdot-12\)

\(=-9\)

\(\dfrac{15}{34}-\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{15}{17}-\dfrac{2}{3}\)

\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)-\left(\dfrac{7}{21}+\dfrac{2}{3}\right)-\dfrac{15}{17}\)

\(=1-\left(\dfrac{7}{21}+\dfrac{14}{21}\right)-\dfrac{15}{17}\)

\(=1-1-\dfrac{15}{17}\)

\(=-\dfrac{15}{17}\)

nhanh

\(\left(\dfrac{3}{5}\right)^{10}\cdot\left(\dfrac{5}{3}\right)^{10}-\dfrac{13^4}{39^4}+2014^0\\ =\left(\dfrac{3\cdot5}{5\cdot3}\right)^{10}-\dfrac{13^4}{\left(3\cdot13\right)^4}+1\\ =\left(\dfrac{15}{15}\right)^{10}-\dfrac{13^4}{3^4\cdot13^4}+1\\ =1^{10}-\dfrac{1}{81}+1\\ =\dfrac{80}{81}+1\\ =\dfrac{161}{81}\)