Given xgt 0 rewrite the following expression in simplest radical form. sqrt [4](256x^8)cdot sqrt [3](125x^2) Answer Attempt 2 out of 2 square

To simplify the expression $\sqrt [4]{256x^{8}}\cdot \sqrt [3]{125x^{2}}$, we need to break it down into simpler parts.<br /><br />First, let's simplify $\sqrt [4]{256x^{8}}$:<br />$\sqrt [4]{256x^{8}} = \sqrt [4]{256} \cdot \sqrt [4]{x^{8}}$<br /><br />Since $256 = 4^4$, we have:<br />$\sqrt [4]{256} = 4$<br /><br />And since $x^8 = (x^2)^4$, we have:<br />$\sqrt [4]{x^{8}} = x^2$<br /><br />So, $\sqrt [4]{256x^{8}} = 4x^2$<br /><br />Next, let's simplify $\sqrt [3]{125x^{2}}$:<br />$\sqrt [3]{125x^{2}} = \sqrt [3]{125} \cdot \sqrt [3]{x^{2}}$<br /><br />Since $125 = 5^3$, we have:<br />$\sqrt [3]{125} = 5$<br /><br />And since $x^2 = (x^{1/3})^3$, we have:<br />$\sqrt [3]{x^{2}} = x^{2/3}$<br /><br />So, $\sqrt [3]{125x^{2}} = 5x^{2/3}$<br /><br />Now, we can multiply the two simplified expressions together:<br />$4x^2 \cdot 5x^{2/3} = 20x^{2 + 2/3} = 20x^{8/3}$<br /><br />Therefore, the simplified form of the given expression is $20x^{8/3}$.