You have to calculate digit at only unit's place. So, you can write them as
7^60 * 3^60
Now, there you should know about CYCLICITY (it means the power after which a number shows same unit digit)....
cyclicity for both 3 & 7 is 4
Now, you have to divide powers by 4 and need to focus on remainder. It would become 0 as the power is 60 here.
so, 1*1 =1
1 will be in unit place.
NICE QUESTION!!!
DID YOU UNDERSTAND??
