4.284 Вычислите степень дробного числа: a) (-); б) (); в) (); г) (-1); д) (-2); e) (-1)

Ответ:

a)

\[\left(-\frac{1}{2}\right)^{3} = -\frac{1^{3}}{2^{3}} = -\frac{1}{8}\]

б)

\[\left(-\frac{2}{3}\right)^{4} = \frac{2^{4}}{3^{4}} = \frac{16}{81}\]

в)

\[\left(-\frac{5}{4}\right)^{2} = \frac{5^{2}}{4^{2}} = \frac{25}{16} = 1\frac{9}{16}\]

г)

\[\left(-1\frac{1}{2}\right)^{3} = \left(-\frac{3}{2}\right)^{3} = -\frac{3^{3}}{2^{3}} = -\frac{27}{8} = -3\frac{3}{8}\]

д)

\[\left(-2\frac{1}{3}\right)^{2} = \left(-\frac{7}{3}\right)^{2} = \frac{7^{2}}{3^{2}} = \frac{49}{9} = 5\frac{4}{9}\]

е)

\[\left(-1\frac{2}{3}\right)^{3} = \left(-\frac{5}{3}\right)^{3} = -\frac{5^{3}}{3^{3}} = -\frac{125}{27} = -4\frac{17}{27}\]

Ответ:

a) \[-\frac{1}{8}\]

б) \[ \frac{16}{81}\]

в) \[1\frac{9}{16}\]

г) \[-3\frac{3}{8}\]

д) \[5\frac{4}{9}\]

е) \[-4\frac{17}{27}\]