\[\boxed{\text{4.\ 284}}\]
\[\textbf{а)}\ \left( - \frac{1}{2} \right)^{3} = - \frac{1}{8}\]
\[\textbf{б)}\ \left( - \frac{2}{3} \right)^{4} = \frac{32}{81}\]
\[\textbf{в)}\ \left( - \frac{5}{4} \right)^{2} = \frac{25}{16} = 1\frac{9}{16}\]
\[\textbf{г)}\ \left( - 1\frac{1}{2} \right)^{3} = \left( - \frac{3}{2} \right)^{3} = - \frac{27}{8} =\]
\[= - 3\frac{3}{8}\]
\[\textbf{д)}\ \left( - 2\frac{1}{3} \right)^{2} = \left( - \frac{7}{3} \right)^{2} = \frac{49}{9} = 5\frac{4}{9}\]
\[\textbf{е)}\ \left( - 1\frac{2}{3} \right)^{4} = \left( - \frac{5}{3} \right)^{4} = \frac{625}{81} =\]
\[= 7\frac{58}{81}\]