a)  ${4,5}^{12}\cdot {\left(\frac{4}{9}\right)}^{12}:2^{12}={\left(4,5\cdot \frac{4}{9}:2\right)}^{12}={\left(\frac{9}{2}\cdot \frac{4}{9}\cdot \frac{1}{2}\right)}^{12}={\left(\frac{{\sout{9}}^1}{2}\cdot \frac{4}{{\sout{9}}^1}\cdot \frac{1}{2}\right)}^{12}={\left(\frac{1}{2}\cdot \frac{4}{1}\cdot \frac{1}{2}\right)}^{12}={\left(\frac{4}{4}\right)}^{12}=1^{12}=1$