A)   $\begin{array}{rcl} & & {\mathrm{w}}^{1010}+{\mathrm{w}}^{2020}\\ & & {\left({\mathrm{w}}^3\right)}^{336}·{\mathrm{w}}^2+{\left({\mathrm{w}}^3\right)}^{673}\mathrm{w}\\ & =& {\mathrm{w}}^2+\mathrm{w}\\ & =& -1\end{array}$

B)   $\begin{array}{rcl} & & \left(1+\mathrm{w}-{\mathrm{w}}^2\right) \left(1-\mathrm{w}+{\mathrm{w}}^2\right)\\ & & \left(-{\mathrm{w}}^2-{\mathrm{w}}^2\right) \left(-\mathrm{w}-\mathrm{w}\right)\\ & =& \left(-2{\mathrm{w}}^2\right) \left(-2\mathrm{w}\right)\\ & =& 4{\mathrm{w}}^3\\ & =& 4\end{array}$

C)   $\begin{array}{rcl} & & {\left(2+{\mathrm{w}}^2+{\mathrm{w}}^4\right)}^5\\ & =& {\left(2+\mathrm{w}+{\mathrm{w}}^2\right)}^5\\ & =& {\left(1+\left(1+\mathrm{w}+{\mathrm{w}}^2\right)\right)}^5\\ & =& {\left(1+0\right)}^5\\ & =& 1\end{array}$

D)   $\begin{array}{rcl} & & {\left(3+5\mathrm{w}+3{\mathrm{w}}^2\right)}^3\\ & & {\left(3\left(1+\mathrm{w}+{\mathrm{w}}^2\right)+2\mathrm{w}\right)}^3\\ & & {\left(3\left(0\right)+2\mathrm{w}\right)}^3\\ & =& 2^3 {\mathrm{w}}^3\\ & =& 8\left(1\right)=8\\ \mathrm{A} & \to & \mathrm{III} \mathrm{B}\to \mathrm{IV} \mathrm{C}\to \mathrm{II} \mathrm{D}\to \mathrm{V}\end{array}$

Option (3) correct.