Given xgt 0 , simplify sqrt [3](8x^30) completely. Answer Attemptiout of 3 square

To simplify the expression $\sqrt[3]{8x^{30}}$, we need to apply the properties of cube roots and exponents.<br /><br />First, let's rewrite the expression inside the cube root:<br />\[ 8x^{30} \]<br /><br />We know that $8$ can be written as $2^3$, so we have:<br />\[ 8x^{30} = (2^3)x^{30} \]<br /><br />Now, we can use the property of exponents that states $(a^m)^n = a^{mn}$:<br />\[ (2^3)x^{30} = 2^3 \cdot x^{30} \]<br /><br />Next, we apply the cube root to the entire expression:<br />\[ \sqrt[3]{2^3 \cdot x^{30}} \]<br /><br />Using the property of cube roots that states $\sqrt[3]{a \cdot b} = \sqrt[3]{a} \cdot \sqrt[3]{b}$, we can separate the terms:<br />\[ \sqrt[3]{2^3} \cdot \sqrt[3]{x^{30}} \]<br /><br />Now, we simplify each term separately:<br />\[ \sqrt[3]{2^3} = 2 \]<br />\[ \sqrt[3]{x^{30}} = x^{30/3} = x^{10} \]<br /><br />Putting it all together, we get:<br />\[ 2 \cdot x^{10} \]<br /><br />Therefore, the simplified form of $\sqrt[3]{8x^{30}}$ is:<br />\[ \boxed{2x^{10}} \]