Unit digit Calculation for (49)^53 - (33)^47
The unit digit of a number is determined by the value of the number modulo 10. In this case, we need to find the unit digit of (49)^53 - (33)^47.

Calculating (49)^53
- The unit digit of 49 is 9. So, we need to find the unit digit of 9^53.
- The pattern of the unit digits of powers of 9 repeats every 2 powers: 9^1 = 9, 9^2 = 81, 9^3 = 729, 9^4 = 6561, and so on.
- Since 53 is an odd number, the unit digit of 9^53 will be the same as the unit digit of 9^1, which is 9.

Calculating (33)^47
- The unit digit of 33 is 3. So, we need to find the unit digit of 3^47.
- The pattern of the unit digits of powers of 3 repeats every 4 powers: 3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, and so on.
- Since 47 is 3 more than a multiple of 4, the unit digit of 3^47 will be the same as the unit digit of 3^3, which is 7.

Subtracting the Unit Digits
- The unit digit of (49)^53 is 9, and the unit digit of (33)^47 is 7.
- Subtracting the unit digits, we get 9 - 7 = 2.
Therefore, the unit digit obtained for (49)^53 - (33)^47 is 2.