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Ответ:
а) \(\dfrac{2}{7}\cdot\dfrac{1}{2}=\dfrac{1}{7}\).
б) \(\dfrac{3}{5}\cdot\dfrac{5}{7}=\dfrac{3}{7}\).
в) \(\dfrac{3}{5}\cdot\dfrac{7}{9}=\dfrac{7}{15}\).
г) \(\dfrac{6}{7}\cdot1\dfrac{2}{3}=\dfrac{6}{7}\cdot\dfrac{5}{3}=\dfrac{10}{7}=1\dfrac{3}{7}\).
д) \(2\dfrac{1}{5}\cdot\dfrac{5}{11}=\dfrac{11}{5}\cdot\dfrac{5}{11}=1\).
е) \(3\dfrac{2}{5}\cdot1\dfrac{3}{17}=\dfrac{17}{5}\cdot\dfrac{20}{17}=4\).
ж) \(3^2=9\).
з) \(4^3=64\).
и) \(\left(\dfrac{2}{3}\right)^2=\dfrac{4}{9}\).
к) \(\left(\dfrac{3}{4}\right)^3=\dfrac{27}{64}\).
л) \(\left(1\dfrac{1}{2}\right)^3=\left(\dfrac{3}{2}\right)^3=\dfrac{27}{8}=3\dfrac{3}{8}\).
м) \(\left(2\dfrac{1}{3}\right)^2=\left(\dfrac{7}{3}\right)^2=\dfrac{49}{9}=5\dfrac{4}{9}\).
н) \(\dfrac{3}{5}:\dfrac{1}{5}=3\).
о) \(\dfrac{2}{15}:\dfrac{8}{5}=\dfrac{2}{15}\cdot\dfrac{5}{8}=\dfrac{1}{12}\).
п) \(\dfrac{5}{8}:\left(-\dfrac{15}{4}\right)=\dfrac{5}{8}\cdot\left(-\dfrac{4}{15}\right)=-\dfrac{1}{6}\).
р) \(\left(-1\dfrac{1}{3}\right):\left(2\dfrac{1}{3}\right)=\left(-\dfrac{4}{3}\right):\dfrac{7}{3}=-\dfrac{4}{7}\).
с) \(5\dfrac{1}{3}:\dfrac{8}{9}=\dfrac{16}{3}\cdot\dfrac{9}{8}=6\).
т) \(\left(-3\dfrac{1}{4}\right):\left(-5\dfrac{3}{2}\right)=\left(-\dfrac{13}{4}\right):\left(-\dfrac{13}{2}\right)=\dfrac{1}{2}\).
у) \(\left(-4\dfrac{1}{6}\right)\cdot5=\left(-\dfrac{25}{6}\right)\cdot5=-\dfrac{125}{6}=-20\dfrac{5}{6}\).
ф) \(6:\left(-1\dfrac{1}{2}\right)=6:\left(-\dfrac{3}{2}\right)=-4\).
Ответ: а) \(\frac17\); б) \(\frac37\); в) \(\frac7{15}\); г) \(1\frac37\); д) \(1\); е) \(4\); ж) \(9\); з) \(64\); и) \(\frac49\); к) \(\frac{27}{64}\); л) \(3\frac38\); м) \(5\frac49\); н) \(3\); о) \(\frac1{12}\); п) \(-\frac16\); р) \(-\frac47\); с) \(6\); т) \(\frac12\); у) \(-20\frac56\); ф) \(-4\).
