$a)\frac{2181.729+243.81.27}{3^2.9^2.234+18.54.162}$
$=\frac{2181.729+243.3.81.9}{9.81.243+18.54.2.81.9+723.729}$
$=\frac{7281.729+729.729}{729.234+1944.729+723.729}$
$=\frac{729.(2181+729)}{729.(234+1944+723)}$
$=\frac{729.2190}{729.2901}$
$=\frac{970}{967}$
$b)\frac{5.4^15-9^9-4.3^20.8^9}{5.2^9.6^19-7.2^29.27^6}$
$=\frac{2^{29}.3^{18}.(5.2-3^2)}{5.2^{28}.3^{19}-7.2^{19}.3^{18}}$
$=\frac{2^{29}.3^{18}.1}{2^{28}.3^{18}.(5.3-7.2)}$
$=\frac{2^{29}.3^{18}}{2^{28}.3^{18}}=2$