Given xgt 0 rewrite the following expression in simplest radical form. sqrt [3](27x^2)cdot sqrt [4](81x) Answer Attemptiout of 2 square

To simplify the given expression, we need to rewrite it in terms of its prime factors and then simplify the radicals.<br /><br />Given expression: $\sqrt [3]{27x^{2}}\cdot \sqrt [4]{81x}$<br /><br />Step 1: Rewrite the expression in terms of prime factors.<br />$\sqrt [3]{27x^{2}} = \sqrt [3]{3^3 \cdot x^2} = 3x^{2/3}$<br />$\sqrt [4]{81x} = \sqrt [4]{3^4 \cdot x} = 3x^{1/4}$<br /><br />Step 2: Multiply the simplified expressions.<br />$3x^{2/3} \cdot 3x^{1/4} = 9x^{2/3 + 1/4} = 9x^{11/12}$<br /><br />Therefore, the simplified form of the given expression is $9x^{11/12}$.