$a)5^{-3}\cdot 5^4\cdot {\left(5^3\right)}^{-2}:\left({\left(5^3\right)}^{-4}:{25}^{-3}\right)=$   $5^{-3}\cdot 5^4\cdot 5^{-6}:\left(5^{-12}:{\left(5^2\right)}^{-3}\right)=$  

$=5^{-3+4+\left(-6\right)}:\left(5^{-12}:5^{-6}\right)=5^{-5}:5^{-12-\left(-6\right)}=5^{-5}:5^{-12+6}=5^{-5}:5^{-6}=$