$a)\,\,\frac{{{15.4}^{12}}{{.9}^{7}}-{{4.3}^{15}}{{.8}^{8}}}{{{19.2}^{24}}{{.3}^{14}}-{{6.4}^{12}}{{.27}^{5}}}$

$=\frac{3.5.{{\left( {{2}^{2}} \right)}^{12}}.{{\left( {{3}^{2}} \right)}^{7}}-{{2}^{2}}{{.3}^{15}}.{{\left( {{2}^{3}} \right)}^{8}}}{{{19.2}^{24}}{{.3}^{14}}-2.3.{{\left( {{2}^{2}} \right)}^{12}}.{{\left( {{3}^{3}} \right)}^{5}}}$

$=\frac{{{3}^{15}}{{.5.2}^{24}}-{{2}^{2}}{{.3}^{15}}{{.2}^{24}}}{{{19.2}^{24}}{{.3}^{14}}-{{2.3.2}^{24}}{{.3}^{15}}}$

$=\frac{{{3}^{15}}{{.2}^{24}}.\left( 5-{{2}^{2}} \right)}{{{3}^{14}}{{.2}^{24}}.\left( 19-{{2.3}^{2}} \right)}$

$=\frac{3.1}{1}=3$

$b)\frac{{{3}^{15}}{{.2}^{22}}+{{6}^{16}}{{.4}^{4}}}{{{2.9}^{9}}{{.8}^{7}}-{{7.27}^{5}}{{.2}^{23}}}$

$=\frac{{{3}^{15}}{{.2}^{22}}+{{2}^{16}}{{.3}^{16}}.{{\left( {{2}^{2}} \right)}^{4}}}{2.{{\left( {{3}^{2}} \right)}^{9}}.{{\left( {{2}^{3}} \right)}^{7}}-7.{{\left( {{3}^{3}} \right)}^{5}}{{.2}^{23}}}$

$=\frac{{{3}^{15}}{{.2}^{22}}+{{2}^{24}}{{.3}^{16}}}{{{2}^{22}}{{.3}^{18}}-{{7.3}^{15}}{{.2}^{23}}}$

$=\frac{{{3}^{15}}{{.2}^{22}}.\left( 1+{{2}^{2}}.3 \right)}{{{2}^{22}}{{.3}^{15}}.\left( {{3}^{3}}-7.2 \right)}$

$=\frac{1+12}{27-14}$

$=\frac{13}{13}$

$=1$