Question Given xgt 0 rewrite the following expression in simplest radical form. sqrt [4](16x^2)cdot sqrt [3](216x^11) Answer Attemptiout of 2 square

## Step 1<br />The given expression is \(\sqrt [4]{16x^{2}}\cdot \sqrt [3]{216x^{11}}\). We need to simplify this expression by rewriting it in simplest radical form.<br /><br />## Step 2<br />First, we simplify \(\sqrt [4]{16x^{2}}\). The fourth root of 16 is 2, and the fourth root of \(x^{2}\) is \(x^{1/2}\). Therefore, \(\sqrt [4]{16x^{2}}\) simplifies to \(2x^{1/2}\).<br /><br />## Step 3<br />Next, we simplify \(\sqrt [3]{216x^{11}}\). The cube root of 216 is 6, and the cube root of \(x^{11}\) is \(x^{11/3}\). Therefore, \(\sqrt [3]{216x^{11}}\) simplifies to \(6x^{11/3}\).<br /><br />## Step 4<br />Finally, we multiply the two simplified expressions together. This gives us \(2x^{1/2} \cdot 6x^{11/3}\).<br /><br />## Step 5<br />We can simplify this further by adding the exponents of \(x\), since the bases are the same. This gives us \(12x^{1/2 + 11/3}\).<br /><br />## Step 6<br />Adding the fractions \(1/2\) and \(11/3\) gives us \(1/2 + 11/3 = 3/6 + 22/6 = 25/6\). Therefore, the final simplified expression is \(12x^{25/6}\).