What is the simplified form of the following expression? Assume \( x>0 \) \( \sqrt[4]{\frac{3}{2 x}} \)

To simplify the expression \( \sqrt[4]{\frac{3}{2 x}} \), we can rewrite it as: \[ \sqrt[4]{\frac{3}{2}} \cdot \sqrt[4]{\frac{1}{x}}. \] This can be further expressed as: \[ \sqrt[4]{\frac{3}{2}} \cdot \frac{1}{\sqrt[4]{x}}. \] Thus, the simplified form of the expression is: \[ \frac{\sqrt[4]{3}}{\sqrt[4]{2} \cdot \sqrt[4]{x}}. \]