Find the unit digit in the product : $${\left( {4387} \right)^{245}}$$   $$ \times {\left( {621} \right)^{72}}$$

Solution(By Examveda Team)

\[\begin{gathered} {\text{ unit place}} \hfill \\ \left[ \begin{gathered} {7^1} \to 7 \to 7 \hfill \\ {7^2} \to 49 \to 9 \hfill \\ {7^3} \to 343 \to 3 \hfill \\ {7^4} \to 2401 \to 1 \hfill \\ \end{gathered} \right]{\text{cycle }} \hfill \\ \end{gathered} \]
$$\eqalign{ & {\left( {4387} \right)^{245}}\,\,\,\,\, \times \,\,\,\,\,{\left( {621} \right)^{72}} \cr & \,\,\,\,\mathop {{{\left( 7 \right)}^{245}}\,\,\,\,\,\,\,\,}\limits^ \downarrow \times \,\,\,\,\,\,\,\,\,{\left( 1 \right)^{72}} \cr & \,\,\,\,\mathop {{{\left( 7 \right)}^{4 \times 61 + 1}}\,\,\,}\limits^ \downarrow \times \,\,\,\,\,\,\,\,\,\,\,1 \cr & \,\mathop {{{\left( 7 \right)}^{4 \times 61}} \times 7\,\,}\limits^ \downarrow \times \,\,\,\,\,\,\,\,\,\,\,1 \cr & \,\,\,\,\,\,\mathop {{{\left( 1 \right)}^{61 }\times 7}}\limits^ \downarrow \,\,\,\,\, \times \,\,\,\,\,\,\,\,\,\,\,1 \cr} $$
unit digit = 7