a) $2^4$ , $4^2={\left(2^2\right)}^2=2^4$

$2^4=4^2$

b) $2^0=1$   $,$ $0^2=0$

$2^0>0^2$

c) $2^{2^3}=2^8$ , ${\left(2^2\right)}^3=2^6$

$2^{2^3}>{\left(2^2\right)}^3$

d) $4^{2^2}=4^4$ , ${\left(4^2\right)}^2=4^4$

$4^{2^2}={\left(4^2\right)}^2$

e) $3^{3^3}=3^{27}$ , ${\left(3^3\right)}^2=3^6$

$3^{3^3}>{\left(3^3\right)}^2$