Given xgt 0 , rewrite the following expression in simplest form. sqrt (49x^10)cdot sqrt [3](125x^9) Answer Attemptiout of 2 square

## Step 1<br />The given expression is \(\sqrt {49x^{10}}\cdot \sqrt [3]{125x^{9}}\). We need to simplify this expression.<br /><br />## Step 2<br />We start by simplifying each square root and cube root separately.<br /><br />### \(\sqrt {49x^{10}} = \sqrt {49} \cdot \sqrt {x^{10}} = 7x^{5}\)<br /><br />Here, we have used the property that \(\sqrt {a \cdot b} = \sqrt {a} \cdot \sqrt {b}\) and \(\sqrt {x^{2n}} = x^{n}\).<br /><br />## Step 3<br />Similarly, we simplify the cube root.<br /><br />### \(\sqrt [3]{125x^{9}} = \sqrt [3]{125} \cdot \sqrt [3]{x^{9}} = 5x^{3}\)<br /><br />Here, we have used the property that \(\sqrt [n]{a \cdot b} = \sqrt [n]{a} \cdot \sqrt [n]{b}\) and \(\sqrt [n]{x^{n}} = x\).<br /><br />## Step 4<br />Now, we multiply the simplified expressions.<br /><br />### \(7x^{5} \cdot 5x^{3} = 35x^{8}\)<br /><br />Here, we have used the property that \(a^{m} \cdot a^{n} = a^{m+n}\).