1197. Вычислите: а) \(\left(\frac{1}{3}\right)^{-3}\); б) \(\left(\frac{3}{4}\right)^{-1}\); в) 0,01⁻²; г) \(\left(1\frac{2}{3}\right)^{-4}\); д) \(\left(-1\frac{1}{3}\right)^{-5}\).

Решение:

• а) \(\left(\frac{1}{3}\right)^{-3}\) = \(\left(\frac{3}{1}\right)^{3}\) = 3³ = 27
• б) \(\left(\frac{3}{4}\right)^{-1}\) = \(\frac{4}{3}\)
• в) 0,01⁻² = \(\left(\frac{1}{100}\right)^{-2}\) = 100² = 10000
• г) \(\left(1\frac{2}{3}\right)^{-4}\) = \(\left(\frac{5}{3}\right)^{-4}\) = \(\left(\frac{3}{5}\right)^{4}\) = \(\frac{3^4}{5^4}\) = \(\frac{81}{625}\)
• д) \(\left(-1\frac{1}{3}\right)^{-5}\) = \(\left(-\frac{4}{3}\right)^{-5}\) = \(\left(-\frac{3}{4}\right)^{5}\) = \(-\frac{3^5}{4^5}\) = \(-\frac{243}{1024}\)

Ответ: а) 27; б) \(\frac{4}{3}\); в) 10000; г) \(\frac{81}{625}\); д) \(-\frac{243}{1024}\).