Find the unit place digit in (192)
102
+(193)
103
.

To find the unit place digit of (192)
102
+(193)
103
, we only need to look at the unit digits of the base numbers and the cyclicity of their powers.

For (192)
102
:
The unit digit of the base is 2.
The cyclicity of 2 is 4 (2
1
=2, 2
2
=4, 2
3
=8, 2
4
=16).
Divide the exponent 102 by 4:

4
102
​
=25 with a remainder of 2
So, the unit digit of (192)
102
is the same as the unit digit of 2
2
=4.

For (193)
103
:
The unit digit of the base is 3.
The cyclicity of 3 is 4 (3
1
=3, 3
2
=9, 3
3
=27, 3
4
=81).
Divide the exponent 103 by 4:

4
103
​
=25 with a remainder of 3
So, the unit digit of (193)
103
is the same as the unit digit of 3
3
=27, which is 7.

Total Unit Digit:
Sum of the unit digits =4+7=11.
Therefore, the unit place digit is 1.