Given xgt 0 rewrite the following expression in simplest radical form. sqrt (25x^8)cdot sqrt [4](16x) Answer Attempt 1out of 2 square

## Step 1<br />The given expression is \(\sqrt {25x^{8}}\cdot \sqrt [4]{16x}\). We need to simplify this expression.<br /><br />## Step 2<br />We start by simplifying each square root separately. The square root of \(25x^{8}\) is \(5x^{4}\), because \(5x^{4}\) squared equals \(25x^{8}\).<br /><br />### \(\sqrt {25x^{8}} = 5x^{4}\)<br /><br />## Step 3<br />Similarly, the fourth root of \(16x\) is \(2x^{1/4}\), because \((2x^{1/4})^{4}\) equals \(16x\).<br /><br />### \(\sqrt [4]{16x} = 2x^{1/4}\)<br /><br />## Step 4<br />Now, we multiply the two simplified expressions together. This gives us \(10x^{17/4}\).<br /><br />### \(5x^{4} \cdot 2x^{1/4} = 10x^{17/4}\)