$a)5^{-3}\cdot {\left(\frac{1}{2}\right)}^{-4}=\frac{1}{5^3}\cdot 2^4=\frac{1}{125}\cdot 16=\frac{16}{125}$

$b)3^6\cdot {\left(1\frac{1}{2}\right)}^{-5}=3^6\cdot {\left(\frac{3}{2}\right)}^{-5}=3^6\cdot {\left(\frac{2}{3}\right)}^5={\sout{729}}^3\cdot \frac{32}{{\sout{243}}^1}=96$ $b)3^6\cdot {\left(1\frac{1}{2}\right)}^{-5}=3^6\cdot {\left(\frac{3}{2}\right)}^{-5}=3^6\cdot {\left(\frac{2}{3}\right)}^5={\sout{729}}^3\cdot \frac{32}{{\sout{243}}^1}=96$

$c){10}^{-4}\cdot {0,01}^{-2}=\frac{1}{{10}^4}\cdot {\left(\frac{1}{100}\right)}^{-2}=\frac{1}{10000}\cdot {100}^2=\frac{1}{10000}\cdot 10000=\frac{10000}{10000}=1$

$d)9^{-2}:{\left(\frac{1}{3}\right)}^{-1}=\frac{1}{9^2}:3=\frac{1}{81}\cdot \frac{1}{3}=\frac{1}{243}$

$e){\left(\frac{1}{3}\right)}^{-1}:9^{-2}=3:\frac{1}{9^2}=3:\frac{1}{81}=3\cdot 81=243$

$f){0,01}^{-3}:{10}^{-2}={\left(\frac{1}{100}\right)}^{-3}:\frac{1}{{10}^2}={100}^3:\frac{1}{100}=1000000:\frac{1}{100}=1000000\cdot 100=100000000$