59. Упростите и вычислите: 1) \(9^{\frac25}\cdot27^{\frac25}\); 2) \(7^{\frac23}\cdot49^{\frac23}\); 3) \(144^{\frac34}:9^{\frac34}\); 4) \(150^{\frac32}:6^{\frac32}\).

1. \(9^{\frac25}\cdot27^{\frac25}=(9\cdot27)^{\frac25}=243^{\frac25}=(3^5)^{\frac25}=3^2=9\).
2. \(7^{\frac23}\cdot49^{\frac23}=(7\cdot49)^{\frac23}=343^{\frac23}=(7^3)^{\frac23}=7^2=49\).
3. \(144^{\frac34}:9^{\frac34}=\left(\dfrac{144}{9}\right)^{\frac34}=16^{\frac34}=\left(\sqrt[4]{16}\right)^3=2^3=8\).
4. \(150^{\frac32}:6^{\frac32}=\left(\dfrac{150}{6}\right)^{\frac32}=25^{\frac32}=\left(\sqrt{25}\right)^3=5^3=125\).

Ответ: 1) 9; 2) 49; 3) 8; 4) 125.