Given xgt 0 , rewrite the following expression in simplest radical form. sqrt [3](125x^3)cdot sqrt [4](81x) Answer Attemptiout of 2 square

To simplify the given expression, we need to rewrite it in simplest radical form.<br /><br />The given expression is:<br />$\sqrt [3]{125x^{3}}\cdot \sqrt [4]{81x}$<br /><br />Step 1: Simplify the cube root term.<br />$\sqrt [3]{125x^{3}} = \sqrt [3]{125} \cdot \sqrt [3]{x^{3}} = 5x$<br /><br />Step 2: Simplify the fourth root term.<br />$\sqrt [4]{81x} = \sqrt [4]{81} \cdot \sqrt [4]{x} = 3\sqrt [4]{x}$<br /><br />Step 3: Multiply the simplified terms.<br />$5x \cdot 3\sqrt [4]{x} = 15x\sqrt [4]{x}$<br /><br />Therefore, the simplified expression is:<br />$\boxed{15x\sqrt [4]{x}}$