Given xgt 0 rewrite the following expression in simplest form. sqrt [4](16x^6)cdot sqrt (144x^11) Answer Attemptiout of 2 square

## Step 1<br />The given expression is \(\sqrt [4]{16x^{6}}\cdot \sqrt {144x^{11}}\). We need to simplify this expression.<br /><br />## Step 2<br />We can rewrite the expression by using the property of exponents, which states that \(a^{m/n} = n\sqrt{a^m}\).<br /><br />### \(\sqrt [4]{16x^{6}} = (16x^{6})^{1/4}\)<br />### \(\sqrt {144x^{11}} = (144x^{11})^{1/2}\)<br /><br />## Step 3<br />Next, we simplify the expression by applying the power of a power rule, which states that \((a^m)^n = a^{mn}\).<br /><br />### \((16x^{6})^{1/4} = 16^{1/4} \cdot (x^{6})^{1/4} = 2x^{3/2}\)<br />### \((144x^{11})^{1/2} = 144^{1/2} \cdot (x^{11})^{1/2} = 12x^{11/2}\)<br /><br />## Step 4<br />Finally, we multiply the two simplified expressions together.<br /><br />### \(2x^{3/2} \cdot 12x^{11/2} = 24x^{7}\)