Units Digit

The units digit for powers of three is: 3,9,7,1,3... The 19th number will be 7.

The pattern for 9 is: 9,1,9... and the thirteenth number will be 9

Then we have 7*9, which has a units digit of 3

Powers of 13 (starting with 13^1) end in

3, 9, 7, 1    a cycle of  4

So

13^19  ends in 7

Powers of 19  (starting with 19^1) end in

9, 1      a cycle of 2

So

19^13  ends in 9

So

13^19 * 19^13  ends in

7  * 9  =     ...3