Вычислите: (1/2)^2 (1/2)^3 (1/2)^4 (2/3)^3 (4/5)^2 (1/2)^2 (1/3)^2 (1/3)^3 (2 1/2)^2 (4/3)^2 (5/5)^2 (1/2)^5

Решение:

• \( \left(\frac{1}{2}\right)^2 = \frac{1}{4} \)
• \( \left(\frac{1}{2}\right)^3 = \frac{1}{8} \)
• \( \left(\frac{1}{2}\right)^4 = \frac{1}{16} \)
• \( \left(\frac{2}{3}\right)^3 = \frac{8}{27} \)
• \( \left(\frac{4}{5}\right)^2 = \frac{16}{25} \)
• \( \left(\frac{1}{2}\right)^2 = \frac{1}{4} \)
• \( \left(\frac{1}{3}\right)^2 = \frac{1}{9} \)
• \( \left(\frac{1}{3}\right)^3 = \frac{1}{27} \)
• \( \left(2\frac{1}{2}\right)^2 = \left(\frac{5}{2}\right)^2 = \frac{25}{4} \)
• \( \left(\frac{4}{3}\right)^2 = \frac{16}{9} \)
• \( \left(5\frac{1}{5}\right)^2 = \left(\frac{26}{5}\right)^2 = \frac{676}{25} \)
• \( \left(\frac{1}{2}\right)^5 = \frac{1}{32} \)

Ответ: \( \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{8}{27}, \frac{16}{25}, \frac{1}{4}, \frac{1}{9}, \frac{1}{27}, \frac{25}{4}, \frac{16}{9}, \frac{676}{25}, \frac{1}{32} \).