The units digit of 20132013 is the same as the units digit of 32013.
The units digit of 34 = units digit of 81 = 1
So units digit of 32013 = 32012+1 = 34*503+1 = 34*503 *31 = 1503*3 = 3
Power 2: units digit 9. Multiply by 49 again to get power 4: units digit 1. So every 4th power gives units digit 1. So 16th power has units digit 1, so the previous power, the 15th must have units digit 3.
It is 4.
It is 8.
1
3
1
it is 3
7
6.
3 to a power divisible by 4 will have a units digit of 1.The powers of 3 are 3, 9, 27, 81 ... obviously, the next one will have a units digit of 1x3 or 3, the next one will have a units digit of 3x3 or 9, the next one will have a units digit of 7 (because 9x3 is 27), the next one will have a units digit of 1 (because 7x3 is 21), and then the cycle starts over with a units digit of 3 again.
9
61,886,548,790,943,213,277,031,694,336