9) Выполните действия (\frac{1}{2}-\frac{1}{3})^{3}:(\frac{1}{3}-\frac{1}{4})^{2}\cdot (\frac{3}{2})^{2}.

Выполним действия (\frac{1}{2}-\frac{1}{3})^{3}:(\frac{1}{3}-\frac{1}{4})^{2}\cdot (\frac{3}{2})^{2}.

Сначала вычислим в скобках:

\frac{1}{2}-\frac{1}{3} = \frac{1\cdot 3}{2\cdot 3}-\frac{1\cdot 2}{3\cdot 2} = \frac{3}{6}-\frac{2}{6} = \frac{3-2}{6} = \frac{1}{6}

\frac{1}{3}-\frac{1}{4} = \frac{1\cdot 4}{3\cdot 4}-\frac{1\cdot 3}{4\cdot 3} = \frac{4}{12}-\frac{3}{12} = \frac{4-3}{12} = \frac{1}{12}

Тогда:

(\frac{1}{2}-\frac{1}{3})^{3}:(\frac{1}{3}-\frac{1}{4})^{2}\cdot (\frac{3}{2})^{2} = (\frac{1}{6})^{3}:(\frac{1}{12})^{2}\cdot (\frac{3}{2})^{2} = \frac{1}{6^{3}} : \frac{1}{12^{2}} \cdot \frac{3^{2}}{2^{2}} = \frac{1}{216} : \frac{1}{144} \cdot \frac{9}{4} = \frac{1}{216} \cdot \frac{144}{1} \cdot \frac{9}{4} = \frac{144 \cdot 9}{216 \cdot 4} = \frac{144 \cdot 9}{24\cdot 9 \cdot 4} = \frac{144}{24\cdot 4} = \frac{144}{96} = \frac{48\cdot 3}{48\cdot 2} = \frac{3}{2} = 1\frac{1}{2}

Ответ: 1\frac{1}{2}