Question

Вычислить:
$(5^{\frac{1}{4}} : 2^{\frac{3}{4}} - 2^{\frac{1}{4}} : 5^{\frac{3}{4}})*\sqrt[4]{1000}$

Answer 1

$\displaystyle\bf\\\Big(5^{\frac{1}{4} } :2^{\frac{3}{4} } -2^{\frac{1}{4} }:5^{\frac{3}{4} } \Big)\cdot\sqrt[4]{1000} =\Big(\sqrt[4]{\frac{5}{2^{3} } } -\sqrt[4]{\frac{2}{5^{3} } } \Big)\cdot\sqrt[4]{1000} = \\\\\\=\Big(\sqrt[4]{\frac{5}{8 } } -\sqrt[4]{\frac{2}{125 } } \Big)\cdot\sqrt[4]{1000} =\sqrt[4]{\frac{5}{8 } } \cdot \sqrt[4]{1000} -\sqrt[4]{\frac{2}{125 } } \cdot\sqrt[4]{1000} =$

$\displaystyle\bf\\=\sqrt[4]{\frac{5\cdot1000}{8 } } -\sqrt[4]{\frac{2\cdot 1000}{125 } } =\sqrt[4]{5\cdot 125} -\sqrt[4]{2\cdot 8} =\sqrt[4]{5^{4} } -\sqrt[4]{2^{4} } =5-2=3$