[tex]\bf \sqrt[4]{144a^{12}b^3}\qquad
\begin{cases}
144=2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\\
\qquad 2^4\cdot 3^2\\
a^{12}=a^{3\cdot 4}\\
\qquad (a^3)^4
\end{cases}\implies \sqrt[4]{2^4\cdot 3^2(a^3)^4b^3}
\\\\\\
2a^3\sqrt[4]{3^2b^3}\implies 2a^3\sqrt[4]{9b^3}[/tex]
