Subtract. Assume that all variables represent positive real numbers. \( \sqrt[3]{81 x}-\sqrt[3]{192 x} \) \( \sqrt[3]{81 x}-\sqrt[3]{192 x}=\square \) (Type an exact answer, using radicals as needed. Simplify your answer.)

To subtract the cube roots, we can rewrite the expression as: \[ \sqrt[3]{81x} - \sqrt[3]{192x} = \sqrt[3]{x} \left(\sqrt[3]{81} - \sqrt[3]{192}\right) \] Now we need to simplify \( \sqrt[3]{81} \) and \( \sqrt[3]{192} \): - \( \sqrt[3]{81} = \sqrt[3]{3^4} = 3 \sqrt[3]{3} \) - \( \sqrt[3]{192} = \sqrt[3]{64 \cdot 3} = \sqrt[3]{64} \cdot \sqrt[3]{3} = 4 \sqrt[3]{3} \) Now we substitute back into the expression: \[ \sqrt[3]{x} \left(3 \sqrt[3]{3} - 4 \sqrt[3]{3}\right) = \sqrt[3]{x} \left(-1 \sqrt[3]{3}\right) \] Thus, we have: \[ \sqrt[3]{81x} - \sqrt[3]{192x} = -\sqrt[3]{3x} \] So the final simplified answer is: \[ \boxed{-\sqrt[3]{3x}} \]