5.24. а) \(\left(\frac{a}{2x}\right)^5\); б) \(\left(\frac{5y}{3}\right)^3\); в) \(\left(\frac{8z}{9}\right)^2\); г) \(\left(\frac{t}{4b}\right)^4\).

Используем правило: \(\left(\frac{m}{n}\right)^k=\frac{m^k}{n^k}\).

1. \(\left(\frac{a}{2x}\right)^5=\frac{a^5}{(2x)^5}=\frac{a^5}{32x^5}\).
2. \(\left(\frac{5y}{3}\right)^3=\frac{(5y)^3}{3^3}=\frac{125y^3}{27}\).
3. \(\left(\frac{8z}{9}\right)^2=\frac{(8z)^2}{9^2}=\frac{64z^2}{81}\).
4. \(\left(\frac{t}{4b}\right)^4=\frac{t^4}{(4b)^4}=\frac{t^4}{256b^4}\).

Ответ: а) \(\frac{a^5}{32x^5}\); б) \(\frac{125y^3}{27}\); в) \(\frac{64z^2}{81}\); г) \(\frac{t^4}{256b^4}\).