Given xgt 0 rewrite the following expression in simplest radical form. sqrt (64x^6)cdot sqrt [3](216x^7) Answer Attempt 1out of 2 square

## Step 1<br />The given expression is \(\sqrt {64x^{6}}\cdot \sqrt [3]{216x^{7}}\). We need to simplify this expression by breaking it down into simpler parts.<br /><br />## Step 2<br />The first part of the expression is \(\sqrt {64x^{6}}\). The square root of 64 is 8 and the square root of \(x^{6}\) is \(x^{3}\). Therefore, \(\sqrt {64x^{6}}\) simplifies to \(8x^{3}\).<br /><br />## Step 3<br />The second part of the expression is \(\sqrt [3]{216x^{7}}\). The cube root of 216 is 6 and the cube root of \(x^{7}\) is \(x^{2}\) with a remainder of \(x\). Therefore, \(\sqrt [3]{216x^{7}}\) simplifies to \(6x^{2}\sqrt [3]{x}\).<br /><br />## Step 4<br />Now, we multiply the simplified parts together. \(8x^{3}\) multiplied by \(6x^{2}\sqrt [3]{x}\) equals \(48x^{5}\sqrt [3]{x}\).