Answer
$a^{15}b^{18}$
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, $(a^{2}b)\times(a^{13}b^{17})=a^{2+13}\times b^{1+17}=a^{15}\times b^{18}=a^{15}b^{18}$.