Given xgt 0 , rewrite the following expression in simplest radical form. sqrt [4](16x^8)cdot sqrt (9x^5) Answer Attemptiout of square

To simplify the given expression, we need to rewrite each radical separately and then multiply the results.<br /><br />First, let's simplify \(\sqrt[4]{16x^8}\):<br /><br />\[<br />\sqrt[4]{16x^8}<br />\]<br /><br />We know that \(16 = 2^4\) and \(x^8 = (x^2)^4\). Therefore,<br /><br />\[<br />\sqrt[4]{16x^8} = \sqrt[4]{2^4 (x^2)^4} = 2x^2<br />\]<br /><br />Next, let's simplify \(\sqrt{9x^5}\):<br /><br />\[<br />\sqrt{9x^5}<br />\]<br /><br />We know that \(9 = 3^2\). Therefore,<br /><br />\[<br />\sqrt{9x^5} = \sqrt{3^2 x^5} = 3\sqrt{x^5}<br />\]<br /><br />Now, we combine the simplified forms:<br /><br />\[<br />2x^2 \cdot 3\sqrt{x^5}<br />\]<br /><br />This simplifies to:<br /><br />\[<br />6x^2 \sqrt{x^5}<br />\]<br /><br />Finally, we can rewrite \(\sqrt{x^5}\) as \(x^{5/2}\):<br /><br />\[<br />6x^2 \sqrt{x^5} = 6x^2 x^{5/2} = 6x^{2 + 5/2} = 6x^{9/2}<br />\]<br /><br />Thus, the simplest radical form of the given expression is:<br /><br />\[<br />\boxed{6x^{9/2}}<br />\]