`1, (3/7 + 1/2)^2`
`= (6/14 + 7/14)^2`
`= (13/14)^2`
`=169/196`
\(2,\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)
\(=\left(\dfrac{9}{12}-\dfrac{10}{12}\right)^2\)
\(=\left(-\dfrac{1}{12}\right)^2\)
\(=\dfrac{1}{144}\)
`3, 2 : (1/2 - 2/3)^3`
`= 2 : (3/6 - 4/6)^3`
`= 2 : (-1/6)^3`
`= 2 : (-1/216)`
`= 2 * -216`
`= -432`
\(4,-\dfrac{2}{5}:1\dfrac{1}{3}-\left(\dfrac{1}{2}\right)^2\)
\(=-\dfrac{2}{5}:\dfrac{4}{3}-\dfrac{1}{4}\)
\(=-\dfrac{2}{5}\cdot\dfrac{3}{4}-\dfrac{1}{4}\)
\(=-\dfrac{1}{5}\cdot\dfrac{3}{2}-\dfrac{1}{4}\)
\(=-\dfrac{3}{10}-\dfrac{1}{4}\)
`= -6/20 - 5/20`
`= -11/20`
\(5,\left(\dfrac{1}{2}-\dfrac{2}{3}+\dfrac{5}{6}\right)\cdot\left(\dfrac{-3}{2}\right)^2\)
`= (3/6 - 4/6 + 5/6) * 9/4`
`= 2/3 * 9/4`
\(=\dfrac{1}{1}\cdot\dfrac{3}{2}\)
`=3/2`
\(6,\left(1+\dfrac{2}{3}-\dfrac{1}{4}\right)\cdot\left(\dfrac{4}{5}-\dfrac{3}{4}\right)^2\)
`= (12/12 - 8/12 - 3/12) * (16/20 - 15/20)^2`
`= 1/12 * (1/20)^2`
`= 1/12 * 1/400`
`= 1/4800`
\(7,\left(1-\dfrac{1}{2}+\dfrac{3}{4}\right)\cdot\left(\dfrac{-2}{5}\right)^2\)
\(=\left(\dfrac{4}{4}-\dfrac{2}{4}+\dfrac{3}{4}\right)\cdot\left(\dfrac{-2}{5}\right)^2\)
\(=\dfrac{5}{4}\cdot\dfrac{4}{25}\)
\(=\dfrac{1}{1}\cdot\dfrac{1}{5}\)
`=1/5`
\(8,\left(\dfrac{-2}{3}\right)^2:\left(\dfrac{7}{18}+\dfrac{2}{9}-\dfrac{1}{2}\right)\)
\(=\left(\dfrac{-2}{3}\right)^2:\left(\dfrac{7}{18}+\dfrac{4}{18}-\dfrac{9}{18}\right)\)
\(=\left(\dfrac{-2}{3}\right)^2:\dfrac{1}{9}\)
\(=\dfrac{4}{9}\cdot9\)
`= 4`
\(9,\left(\dfrac{1}{2}-\dfrac{1}{6}\right)^{10}:\left(\dfrac{1}{3}\right)^8\)
\(=\left(\dfrac{3}{6}-\dfrac{1}{6}\right)^{10}:\left(\dfrac{1}{3}\right)^8\)
\(=\left(\dfrac{1}{3}\right)^{10}:\left(\dfrac{1}{3}\right)^8\)
\(=\left(\dfrac{1}{3}\right)^{10-8}\)
\(=\left(\dfrac{1}{3}\right)^2=\dfrac{1}{9}\)
\(10,\left(\dfrac{6}{5}\right)^{2013}\cdot\left(\dfrac{5}{6}\right)^{2013}+\left(\dfrac{2012}{2013}\right)^0\)
\(=\left(\dfrac{6}{5}\cdot\dfrac{5}{6}\right)^{2013}+\left(\dfrac{2012}{2013}\right)^0\)
\(=1^{2013}+1\)
`= 1 + 1`
`= 2`
