1178. Вычислите: a) (-4)^-3; б) 2,5^-1; в) \( \left( \frac{3}{4} \right)^{-2} \); г) \( \left( 1 \frac{1}{3} \right)^{-3} \); д) -0,4^-4; e) -\( \left( 2 \frac{1}{2} \right)^{-2} \).

Решение:

а) \( (-4)^{-3} \)

\( (-4)^{-3} = \frac{1}{(-4)^3} = \frac{1}{-64} = -\frac{1}{64} \)

б) \( 2.5^{-1} \)

\( 2.5^{-1} = \left( \frac{5}{2} \right)^{-1} = \frac{2}{5} = 0.4 \)

в) \( \left( \frac{3}{4} \right)^{-2} \)

\( \left( \frac{3}{4} \right)^{-2} = \left( \frac{4}{3} \right)^2 = \frac{4^2}{3^2} = \frac{16}{9} = 1 \frac{7}{9} \)

г) \( \left( 1 \frac{1}{3} \right)^{-3} \)

\( 1 \frac{1}{3} = \frac{4}{3} \)

\( \left( \frac{4}{3} \right)^{-3} = \left( \frac{3}{4} \right)^3 = \frac{3^3}{4^3} = \frac{27}{64} \)

д) \( -0.4^{-4} \)

\( -0.4^{-4} = -\left( \frac{2}{5} \right)^{-4} = -\left( \frac{5}{2} \right)^4 = -\frac{5^4}{2^4} = -\frac{625}{16} = -39 \frac{1}{16} \)

е) \( -\left( 2 \frac{1}{2} \right)^{-2} \)

\( 2 \frac{1}{2} = \frac{5}{2} \)

\( -\left( \frac{5}{2} \right)^{-2} = -\left( \frac{2}{5} \right)^2 = -\frac{2^2}{5^2} = -\frac{4}{25} \)

Ответ: а) \( -\frac{1}{64} \); б) \( \frac{2}{5} \); в) \( \frac{16}{9} \); г) \( \frac{27}{64} \); д) \( -\frac{625}{16} \); е) \( -\frac{4}{25} \).