To calculate the radical expression sqrt[3]{x^{12}} to rational exponent form and simplify.

Calculation:
According to exponential rules, ${\displaystyle \sqrt{n}\left\{a\right\}=a^{\frac{1}{n}}}$
Given ${\displaystyle \sqrt{3}\left\{x^{12}\right\}}$
Applying the above rule: where ${\displaystyle a=x^{12},n=3}$
${\displaystyle \sqrt{3}\left\{x^{12}\right\}={\left(x^{12}\right)}^{\frac{1}{3}}}$
According to the power rule, ${\displaystyle {\left(a^m\right)}^n=a^{mn}}$
Applying the above rule: where ${\displaystyle a=x,m=12,n=\frac{1}{3}}$
${\displaystyle \sqrt{3}\left\{x^{12}\right\}=x^{\left(12\right)\left(\frac{1}{3}\right)}}$
${\displaystyle \sqrt{3}\left\{x^{12}\right\}=x^4.}$