$a){\left({10}^3\right)}^4:{\left({10}^2\right)}^5={10}^{12}:{10}^{10}={10}^2=100$

$b){\left({\left(-2\right)}^8\right)}^3:{\left({\left(-2\right)}^3\right)}^6={\left(-2\right)}^{24}:{\left(-2\right)}^{18}={\left(-2\right)}^6={\left({\left(-2\right)}^2\right)}^3=4^3=4\cdot 4\cdot 4=64$