\(a,\left(1-\dfrac{5}{2}+\dfrac{1}{5}\right)^2.\left(2-\dfrac{7}{6}\right)\)
\(=\left(\dfrac{10}{10}-\dfrac{25}{10}+\dfrac{2}{10}\right)^2.\left(\dfrac{12}{6}-\dfrac{7}{6}\right)\)
\(=\left(\dfrac{-13}{10}\right)^2.\dfrac{5}{6}\)
\(=\dfrac{169}{100}.\dfrac{5}{6}\)
\(=\dfrac{169.1}{20.6}\)
\(=\dfrac{169}{120}\)
\(b,2^5:\left(\dfrac{1}{2}-\dfrac{1}{4}\right)^3\)
\(=32:\left(\dfrac{2}{4}-\dfrac{1}{4}\right)^3\)
\(=32:\left(\dfrac{1}{4}\right)^3\)
\(=32:\dfrac{1}{64}\)
\(=32.64\)
\(=2048\)
\(c,\left(\dfrac{2}{3}\right)^6.\left(\dfrac{8}{27}\right)^2\)
\(=\left(\dfrac{2}{3}\right)^6.\left(\dfrac{2^3}{3^3}\right)^2\)
\(=\left(\dfrac{2}{3}\right)^6.\left(\dfrac{2}{3}\right)^6\)
\(=\left(\dfrac{2}{3}\right)^{6+6}\)
\(=\left(\dfrac{2}{3}\right)^{12}\)
\(d,\left(\dfrac{3}{5}\right)^2.\left(\dfrac{-9}{25}\right)^2\)
\(=\left(\dfrac{3}{5}\right)^2.\left(\dfrac{3^2}{5^2}\right)^2\)
\(=\left(\dfrac{3}{5}\right)^2.\left(\dfrac{3}{5}\right)^4\)
\(=\left(\dfrac{3}{5}\right)^{2+4}\)
\(=\left(\dfrac{3}{5}\right)^6\)
\(e,\left(\dfrac{-5}{2}\right)^3:\left(\dfrac{-8}{125}\right)^3\)
\(=\left(\dfrac{-5}{2}\right)^3:\left(\dfrac{\left(-2\right)^3}{5^3}\right)^3\)
\(=\left(\dfrac{-5}{2}\right)^3:\left(\dfrac{-2}{5}\right)^9\)
\(=\left(\dfrac{-5}{2}\right)^3.
\left(\dfrac{-5}{2}\right)^9\)
\(=\left(\dfrac{-5}{2}\right)^{3+9}\)
\(=\left(\dfrac{-5}{2}\right)^{12}\)
