Вычислите: a) (-4)⁻³; б) 2,5⁻¹; в) (3/4)⁻²; г) (1 1/3)⁻³; д) -0,4⁻⁴; е) -(2 1/2)⁻²

Решение:

• а) \( (-4)^{-3} = \frac{1}{(-4)^3} = \frac{1}{-64} = -\frac{1}{64} \)
• б) \( 2,5^{-1} = \frac{1}{2,5} = \frac{1}{\frac{5}{2}} = \frac{2}{5} = 0,4 \)
• в) \( \left(\frac{3}{4}\right)^{-2} = \left(\frac{4}{3}\right)^2 = \frac{4^2}{3^2} = \frac{16}{9} = 1\frac{7}{9} \)
• г) \( \left(1\frac{1}{3}\right)^{-3} = \left(\frac{4}{3}\right)^{-3} = \left(\frac{3}{4}\right)^3 = \frac{3^3}{4^3} = \frac{27}{64} \)
• д) \( -0,4^{-4} = -\left(\frac{4}{10}\right)^{-4} = -\left(\frac{2}{5}\right)^{-4} = -\left(\frac{5}{2}\right)^4 = -\frac{5^4}{2^4} = -\frac{625}{16} = -39\frac{1}{16} \)
• е) \( -(2\frac{1}{2})^{-2} = -\left(\frac{5}{2}\right)^{-2} = -\left(\frac{2}{5}\right)^2 = -\frac{2^2}{5^2} = -\frac{4}{25} \)

Ответ:

• а) \(-\frac{1}{64}\)
• б) \(\frac{2}{5}\) или \(0,4\)
• в) \(1\frac{7}{9}\)
• г) \(\frac{27}{64}\)
• д) \(-39\frac{1}{16}\)
• е) \(-\frac{4}{25}\)