The unit place digit is the last digit (ones place) of a number.
When finding the unit digit of a number raised to a power, only the unit digit of the base number matters.
The base is 37.
Unit digit of 37=7
To find the unit digit of (37)2, only the unit digit of the base needs to be squared:
72=7×7
72=49
The unit digit of 49 is 9.
Therefore, the unit place digit of (37)2 is 9.