Question

$sqrt3{x^{12}} =$

Explanation:

Step1: Recall radical exponent rule

The cube root of a number \( a \) can be written as \( a^{\frac{1}{3}} \), so \( \sqrt[3]{x^{12}}=(x^{12})^{\frac{1}{3}} \).

Step2: Apply power of a power rule

The power of a power rule states that \( (a^m)^n = a^{m\times n} \). Here, \( a = x \), \( m = 12 \), and \( n=\frac{1}{3} \). So we calculate \( 12\times\frac{1}{3}=4 \), which gives \( (x^{12})^{\frac{1}{3}} = x^{4} \).

Answer:

\( x^{4} \)