Answer
$4a^{2}b^{6}$
Work Step by Step
$\sqrt (16a^{4}b^{12})=\sqrt (16\times a^{4}\times b^{12})=\sqrt 16 \times \sqrt (a^{4})\times \sqrt (b^{12})=4a^{2}b^{6}$
$\sqrt 16=4$, because $4^{2}=16$.
$\sqrt (a^{4})=a^{2}$, because $(a^{2})^{2}=a^{2\times2}=a^{4}$.
$\sqrt (b^{12})=b^{6}$, because $(b^{6})^{2}=b^{6\times2}=b^{12}$.