Вопрос:

Вычислите (1.4–1.5): 1.5. 1) (2/4)⁴; 2) (−3/4)⁴; 3) (−2 1/4)⁵; 4) (1 4/5)⁴.

Ответ:

  1. \(\left(\frac{2}{4}\right)^4=\left(\frac{1}{2}\right)^4=\frac{1}{16}\).
  2. \(\left(-\frac{3}{4}\right)^4=\frac{3^4}{4^4}=\frac{81}{256}\).
  3. \(\left(-2\frac{1}{4}\right)^5=\left(-\frac{9}{4}\right)^5=-\frac{9^5}{4^5}=-\frac{59049}{1024}\).
  4. \(\left(1\frac{4}{5}\right)^4=\left(\frac{9}{5}\right)^4=\frac{9^4}{5^4}=\frac{6561}{625}\).

Ответ: 1) \(\frac{1}{16}\); 2) \(\frac{81}{256}\); 3) \(-\frac{59049}{1024}\); 4) \(\frac{6561}{625}\).