Answer
$144a^{38}b^{12}$
Work Step by Step
$(2a^{5}b)^{4}(3a^{9}b^{4})^{2}$
$=(2^{4})[(a^{5})^4](b^{4})(3^{2})[(a^{9})^{2}][(b^{4})^{2}]$
$=(2\times2\times2\times2)(3\times3)(a^{5\times4})(a^{9\times2})(b^{4})(b^{4\times2})$
$=(4\times2\times2)(9)(a^{20})(a^{18})(b^{4})(b^{8})$
$=(8\times2\times9)(a^{20+18})(b^{4+8})$
$=(16\times9)(a^{38})(b^{12})$
$=144a^{38}b^{12}$
