To simplify the radical expression [tex]\(\sqrt[3]{x^{15}}\)[/tex], we need to use the properties of exponents and radicals. The key property we'll use is that the cube root of [tex]\(x^a\)[/tex] can be expressed as [tex]\(x^{a/3}\)[/tex]. Here's a step-by-step solution:
1. The given expression is [tex]\(\sqrt[3]{x^{15}}\)[/tex].
2. Using the property of exponents and radicals, [tex]\(\sqrt[3]{x^a} = x^{a/3}\)[/tex], we can rewrite the expression in exponential form.
3. Substitute [tex]\(a = 15\)[/tex] into [tex]\(x^{a/3}\)[/tex]:
[tex]\[
\sqrt[3]{x^{15}} = x^{15/3}
\][/tex]
4. Simplify the exponent:
[tex]\[
x^{15/3} = x^5
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt[3]{x^{15}}\)[/tex] is [tex]\(x^5\)[/tex].
So, the correct answer is [tex]\(\boxed{x^5}\)[/tex].
