$\frac{2\ast 3^{20}-5\ast 3^{19}}{9^9}=\frac{3^{19}(2\ast 3-5)}{(3^2{)}^9}=\frac{3^{19}(6-5)}{3^{18}}=\frac{3^{19}}{3^{18}}=3$

$\frac{(3\ast 2^{20}+7\ast 2^{19})\ast 52}{(13\ast 8^4{)}^2}=\frac{(2^{19}(3\ast 2+7))\ast 52}{{13}^2\ast 8^8}=\frac{(2^{19}(6+7))\ast 13\ast 4}{{13}^2\ast (2^3{)}^8}=\frac{2^{19}(6+7)\ast 2^2}{13\ast 2^{24}}=\frac{2^{21}\ast 13}{13\ast 2^{24}}=\frac{1}{2^3}=\frac{1}{8}$

$\frac{108\ast 6^7-108\ast 6^6}{{216}^3-{36}^4}=\frac{108\ast 6^6(6-1)}{(6^3{)}^3-(6^2{)}^4}=\frac{3\ast 36\ast 6^6\ast 5}{6^9-6^8}=\frac{3\ast 6^2\ast 6^6\ast 5}{6^8(6-1)}=\frac{3\ast 6^8\ast 5}{6^8\ast 5}=3$

$\frac{(3^{15}+3^{13})\ast 2^9}{(3^{14}+3^{12})\ast 1024}=\frac{3^{13}(3^2+1)\ast 2^9}{3^{12}(3^2+1)\ast 2^{10}}=\frac{3}{2}=1\frac{1}{2}$