a)

$16\cdot 4^{{\log }_{2}8}=4^2\cdot 4^{{\log }_2{2}^3}=4^2\cdot 4^3=4^5=1024$

b)

$3^{-4}\cdot {\left(\frac{1}{9}\right)}^{1+{\log }_{\frac{1}{3}}27}=3^{-4}\cdot {\left(9^{-1}\right)}^{1+{\log }_{\frac{1}{3}}{3}^3}=$