\(\left(3x-\dfrac{1}{2}\right)^3+\dfrac{2.\left(-7\right)^2}{5^3}=1\)
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\(\dfrac{3}{4}\cdot26\dfrac{2}{9}-38\dfrac{2}{9}\cdot\dfrac{3}{4}\)
\(=\dfrac{3}{4}\cdot\left(26\dfrac{2}{9}-38\dfrac{2}{9}\right)\)
\(=\dfrac{3}{4}\cdot\left(26+\dfrac{2}{9}-38-\dfrac{2}{9}\right)\)
\(=\dfrac{3}{4}\cdot-12\)
\(=3\cdot-3\)
\(=-9\)
\(\dfrac{3}{4}\cdot26\dfrac{2}{9}-38\dfrac{2}{9}\cdot\dfrac{3}{4}\)
\(=\dfrac{3}{4}\left(26\dfrac{2}{9}-38\dfrac{2}{9}\right)\)
\(=\dfrac{3}{4}\left[\left(26-38\right)+\left(\dfrac{2}{9}-\dfrac{2}{9}\right)\right]\)
\(=\dfrac{3}{4}\cdot-12\)
\(=-9\)
\(\dfrac{15}{34}-\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{15}{17}-\dfrac{2}{3}\)
\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)-\left(\dfrac{7}{21}+\dfrac{2}{3}\right)-\dfrac{15}{17}\)
\(=1-\left(\dfrac{7}{21}+\dfrac{14}{21}\right)-\dfrac{15}{17}\)
\(=1-1-\dfrac{15}{17}\)
\(=-\dfrac{15}{17}\)
\(\left(\dfrac{3}{5}\right)^{10}\cdot\left(\dfrac{5}{3}\right)^{10}-\dfrac{13^4}{39^4}+2014^0\\ =\left(\dfrac{3\cdot5}{5\cdot3}\right)^{10}-\dfrac{13^4}{\left(3\cdot13\right)^4}+1\\ =\left(\dfrac{15}{15}\right)^{10}-\dfrac{13^4}{3^4\cdot13^4}+1\\ =1^{10}-\dfrac{1}{81}+1\\ =\dfrac{80}{81}+1\\ =\dfrac{161}{81}\)
\(\left(\dfrac{-1}{4}\right)^4=\dfrac{\left(-1\right)^4}{4^4}=\dfrac{1}{256}\)
\(25^6\cdot8^4\)
\(=\left(5^2\right)^6\cdot\left(2^3\right)^4\)
\(=5^{2\cdot6}\cdot2^{3\cdot4}\)
\(=5^{12}\cdot2^{12}\)
\(=\left(5\cdot2\right)^{12}\)
\(=10^{12}\)
\(25^6.8^4\)
\(=\left(5^2\right)^6.\left(2^3\right)^4\)
\(=5^{2.6}.2^{3.4}\)
\(=5^{12}.2^{12}\)
\(=\left(5.2\right)^{12}\)
\(=10^{12}\)