15.35. Вычислите: а) (2 2/3)³ − (1 2/3)³; б) (−1 1/4)³ + (2 1/8)².

а) \(\left(2\frac{2}{3}\right)^3 - \left(1\frac{2}{3}\right)^3 = \left(\frac{8}{3}\right)^3 - \left(\frac{5}{3}\right)^3 = \frac{512}{27} - \frac{125}{27} = \frac{387}{27} = \frac{43}{3} = 14\frac{1}{3}\).

б) \(\left(-1\frac{1}{4}\right)^3 + \left(2\frac{1}{8}\right)^2 = \left(-\frac{5}{4}\right)^3 + \left(\frac{17}{8}\right)^2 = -\frac{125}{64} + \frac{289}{64} = \frac{164}{64} = \frac{41}{16} = 2\frac{9}{16}\).

Ответ: а) \(14\frac{1}{3}\); б) \(2\frac{9}{16}\).