1. Вычислить: 1) (15^(2/3) · 3^(7/3)) / 5^(-1/3); 2) (4/5)^(-2) − (1/27)^(1/3) + 4 · 379^0; 3) (∛128 + ∛(1/4)) : ∛2.

1) \(\dfrac{15^{\frac{2}{3}}\cdot3^{\frac{7}{3}}}{5^{-\frac{1}{3}}}=15^{\frac{2}{3}}\cdot3^{\frac{7}{3}}\cdot5^{\frac{1}{3}}\).

Разложим \(15=3\cdot5\):

\[3^{\frac{2}{3}}5^{\frac{2}{3}}\cdot3^{\frac{7}{3}}\cdot5^{\frac{1}{3}}=3^3\cdot5=27\cdot5=135.\]

2) \(\left(\dfrac45\right)^{-2}=\left(\dfrac54\right)^2=\dfrac{25}{16}\), \(\left(\dfrac1{27}\right)^{\frac13}=\dfrac13\), а \(379^0=1\).

\[\dfrac{25}{16}-\dfrac13+4=\dfrac{75-16+192}{48}=\dfrac{251}{48}.\]

3) \(\sqrt[3]{128}=4\sqrt[3]{2}\), а \(\sqrt[3]{\dfrac14}=\dfrac{1}{2\sqrt[3]{2}}\).

\[\dfrac{4\sqrt[3]{2}+\dfrac1{2\sqrt[3]{2}}}{\sqrt[3]{2}}=4+\dfrac{1}{2\sqrt[3]{4}}.\]

Рационализуем второе слагаемое: \(\dfrac{1}{2\sqrt[3]{4}}=\dfrac{\sqrt[3]{2}}4\). Поэтому результат: \(4+\dfrac{\sqrt[3]{2}}4\).

Ответ: 1) 135; 2) \(\dfrac{251}{48}\); 3) \(4+\dfrac{\sqrt[3]{2}}4\).