a) \(\dfrac{-12}{25}\cdot\dfrac{10}{9}\)
\(=\dfrac{-12\cdot10}{25\cdot9}\)
\(=\dfrac{-4\cdot2}{5\cdot3}\)
\(=\dfrac{-8}{15}\)
b) \(\dfrac{28}{11}:\dfrac{21}{22}\cdot9\)
\(=\dfrac{28}{11}\cdot\dfrac{22}{21}\cdot9\)
\(=\dfrac{28\cdot22\cdot9}{11\cdot21}\)
\(=4\times2\times3\)
\(=24\)
c) \(-\dfrac{10}{21}\cdot\left[\dfrac{9}{15}+\left(\dfrac{3}{5}\right)^2\right]\)
\(=-\dfrac{10}{21}\cdot\left(\dfrac{3}{5}+\dfrac{9}{25}\right)\)
\(=-\dfrac{10}{21}\cdot\left(\dfrac{15}{25}+\dfrac{9}{25}\right)\)
\(=-\dfrac{10}{21}\cdot\dfrac{24}{25}\)
\(=\dfrac{-10\cdot24}{21\cdot25}\)
\(=\dfrac{-2\cdot8}{7\cdot5}\)
\(=\dfrac{-16}{35}\)
d) \(\left(\dfrac{15}{21}:\dfrac{5}{7}\right):\left(\dfrac{6}{5}:2\right)\)
\(=\left(\dfrac{15}{21}\cdot\dfrac{7}{5}\right):\left(\dfrac{6}{5}\cdot\dfrac{1}{2}\right)\)
\(=\left(\dfrac{5}{7}\cdot\dfrac{7}{5}\right):\dfrac{6}{10}\)
\(=1:\dfrac{6}{10}\)
\(=\dfrac{10}{6}\)
\(=\dfrac{5}{3}\)