Answer
$a^{11}b^{20}$
Work Step by Step
Based on the product rule for exponents, we know that $a^{m}\times a^{n}=a^{m+n}$ (where $m$ and $n$ are positive integers and $a$ is a real number).
Therefore, $(a^{7}b^{12})(a^{4}b^{8})=a^{7+4}\times b^{12+8}=a^{11}b^{20}$.