TITLE: the unit digit for $3^{100}\cdot 37^{98}$
QUESTION [6 upvotes]: What is the best  way to know the unit digit for $3^{100}\cdot 37^{98}$

REPLY [2 votes]: Hint $\rm\ mod\ 10\!:\,\ 37\equiv 7\equiv 3^{-1}\!\Rightarrow\: 3^{100}37^{98}\!\equiv 3^{100} 3^{-98}\!\equiv 3^2$