59. 1) \(9^{2/5}\cdot27^{2/5}\); 2) \(7^{2/3}\cdot49^{2/3}\); 3) \(144^{3/4}:9^{3/4}\); 4) \(150^{3/2}:6^{3/2}\).

Используем свойства: \(a^r b^r=(ab)^r\) и \(a^r:b^r=(a:b)^r\).

1. \(9^{2/5}\cdot27^{2/5}=(9\cdot27)^{2/5}=243^{2/5}=(3^5)^{2/5}=3^2=9\).
2. \(7^{2/3}\cdot49^{2/3}=(7\cdot49)^{2/3}=(7^3)^{2/3}=7^2=49\).
3. \(144^{3/4}:9^{3/4}=(144:9)^{3/4}=16^{3/4}=(\sqrt[4]{16})^3=8\).
4. \(150^{3/2}:6^{3/2}=(150:6)^{3/2}=25^{3/2}=(\sqrt{25})^3=125\).