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

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We start with the expression
$$
\sqrt[4]{\frac{x^3}{256}}.
$$

Since the fourth root of a quotient is the quotient of the fourth roots, we can write
$$
\sqrt[4]{\frac{x^3}{256}} = \frac{\sqrt[4]{x^3}}{\sqrt[4]{256}}.
$$

Next, recall that the fourth root of $$a$$ is equivalent to raising $$a$$ to the power of $$\frac{1}{4}$$. Therefore, we have
$$
\sqrt[4]{x^3} = x^{3/4} \quad \text{and} \quad \sqrt[4]{256} = 256^{1/4}.
$$

Since $$256 = 4^4$$, it follows that
$$
256^{1/4} = (4^4)^{1/4} = 4.
$$

Substituting back into our expression, we obtain
$$
\frac{\sqrt[4]{x^3}}{\sqrt[4]{256}} = \frac{x^{3/4}}{4}.
$$

Thus, the simplified expression is
$$
\boxed{\frac{x^{3/4}}{4}}.
$$
$$ \frac{x^{3/4}}{4} $$

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

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