$8^{-3}\ast 2^7=(2^3{)}^{-3}\ast 2^7=2^{-9}\ast 2^7=2^{-9+7}=2^{-2}=\frac{1}{4}$

${27}^{-2}:9^{-4}=(3^3{)}^{-2}:(3^2{)}^{-4}=3^{-6}:3^{-8}=3^{-6-(-8)}=3^{-6+8}=3^2=9$

${100}^{-2}:{1000}^{-5}\ast 0,{01}^6=({10}^2{)}^{-2}:({10}^3{)}^{-5}\ast ({10}^{-2}{)}^6={10}^{-4}:{10}^{-15}\ast {10}^{-12}={10}^{-4-(-15)-12}={10}^{-4+15-12}={10}^{-1}=0,1$

$(2\frac{1}{4}{)}^{-4}\ast ((\frac{2}{3}{)}^3{)}^{-3}=(\frac{9}{4}{)}^{-4}\ast (\frac{2}{3}{)}^{-9}=(\frac{4}{9}{)}^4\ast (\frac{3}{2}{)}^9=(\frac{2^2}{3^2}{)}^4\ast (\frac{3}{2}{)}^9=\frac{2^8}{3^8}\ast \frac{3^9}{2^9}=\frac{3}{2}=1\frac{1}{2}$

${25}^{-4}:(0,2^{-3}{)}^{-2}=\frac{1}{{25}^4}:((\frac{1}{5}{)}^{-3}{)}^{-2}=\frac{1}{(5^2{)}^4}:(\frac{1}{5}{)}^6=\frac{1}{5^8}\ast 5^6=\frac{1}{5^2}=\frac{1}{25}$

$\frac{(-36{)}^{-3}\ast 6^8}{{216}^{-5}\ast (-6{)}^{18}}=\frac{(-6^2{)}^{-3}\ast 6^8}{(6^3{)}^{-5}\ast (-6{)}^{18}}=\frac{(-6{)}^{-6}\ast 6^8}{6^{-15}\ast (-6{)}^{18}}=\frac{6^{-6}\ast 6^8}{6^{-15}\ast 6^{18}}=\frac{6^2}{6^3}=\frac{1}{6}$

$\frac{6^{-10}}{{81}^{-2}\ast {16}^{-3}}=\frac{{81}^2\ast {16}^3}{6^{10}}=\frac{(3^4{)}^2\ast (2^4{)}^3}{(2\ast 3{)}^{10}}=\frac{3^8\ast 2^{12}}{2^{10}\ast 3^{10}}=\frac{2^2}{3^2}=\frac{4}{9}$

$\frac{{14}^5\ast 2^{-7}}{{28}^{-2}\ast 7^8}=\frac{{14}^5\ast {28}^2}{2^7\ast 7^8}=\frac{(2\ast 7{)}^5\ast (2^2\ast 7{)}^2}{2^7\ast 7^8}=\frac{2^5\ast 7^5\ast 2^4\ast 7^2}{2^7\ast 7^8}=\frac{2^9\ast 7^7}{2^7\ast 7^8}=\frac{2^2}{7}=\frac{4}{7}$