$a){\left(0,1\right)}^{-4}\cdot {10}^3={\left(\frac{1}{10}\right)}^{-4}\cdot {10}^3={10}^4\cdot {10}^3={10}^{4+3}={10}^7=10000000$   

$b){\left(0,5\right)}^5\cdot 2^{-3}\cdot {\left(0,5\right)}^{-4}={\left(\frac{1}{2}\right)}^5\cdot 2^{-3}\cdot {\left(\frac{1}{2}\right)}^{-4}=2^{-5}\cdot 2^{-3}\cdot 2^4=2^{-5+\left(-3\right)+4}=2^{-4}=\frac{1}{2^4}=\frac{1}{16}$