Use the quotient rule to simplify. Assume that the variable represents a positive real number. \( \sqrt[4]{\frac{x^{3}}{256}} \) \( \sqrt[4]{\frac{x^{3}}{256}}=\square \) integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.) (Use in

To simplify \( \sqrt[4]{\frac{x^{3}}{256}} \), we can use the quotient rule for radicals: \[ \sqrt[4]{\frac{a}{b}} = \frac{\sqrt[4]{a}}{\sqrt[4]{b}} \] Applying this to our expression gives us: \[ \sqrt[4]{\frac{x^{3}}{256}} = \frac{\sqrt[4]{x^{3}}}{\sqrt[4]{256}} \] Now, since \(256 = 4^4\), we have: \[ \sqrt[4]{256} = 4 \] And for \( \sqrt[4]{x^{3}} \): \[ \sqrt[4]{x^{3}} = x^{3/4} \] Putting it all together, we get: \[ \sqrt[4]{\frac{x^{3}}{256}} = \frac{x^{3/4}}{4} \] Therefore, the final simplified form is: \[ \frac{x^{3/4}}{4} \]