64. $\frac{4 - 2sqrt3{6}}{sqrt3{4}}$

64. $\frac{4 - 2sqrt3{6}}{sqrt3{4}}$

64. $\frac{4 - 2sqrt3{6}}{sqrt3{4}}$

Answer

Explanation:

Step1: Split the fraction

$\frac{4}{\sqrt[3]{4}} - \frac{2\sqrt[3]{6}}{\sqrt[3]{4}}$

Step2: Simplify first term

$4 = 2^2$, $\sqrt[3]{4} = 2^{2/3}$, so $\frac{2^2}{2^{2/3}} = 2^{2 - 2/3} = 2^{4/3} = 2\sqrt[3]{2}$

Step3: Simplify second term

$\frac{\sqrt[3]{6}}{\sqrt[3]{4}} = \sqrt[3]{\frac{6}{4}} = \sqrt[3]{\frac{3}{2}}$, so $2\sqrt[3]{\frac{3}{2}} = \sqrt[3]{12}$

Step4: Combine results

$2\sqrt[3]{2} - \sqrt[3]{12}$

Answer:

$2\sqrt[3]{2} - \sqrt[3]{12}$