Question

simplify the radical expression.
\sqrt3{x^{12}}

Explanation:

Step1: Recall the property of radicals

For a cube root, \(\sqrt[3]{a^n}=a^{\frac{n}{3}}\) when \(a\) is a real number and \(n\) is an integer. Here, our expression is \(\sqrt[3]{x^{12}}\), so we can apply this property.

Step2: Apply the exponent rule

Using the rule \(\sqrt[3]{x^{12}} = x^{\frac{12}{3}}\)

Step3: Simplify the exponent

Simplify \(\frac{12}{3}\) to get \(4\), so \(x^{\frac{12}{3}}=x^{4}\)

Answer:

\(x^{4}\)