What is the last digit of (624)^37 - (256)^38 ?2568

To find the last digit of (624)^37 - (256)^38, we only need to consider the last digit of each base number when raised to its respective power.

Step 1: Consider the last digit of 624, which is 4. The last digit of 4 raised to any power cycles every 2 powers: 4^1 = 4, 4^2 = 6, 4^3 = 4, 4^4 = 6, and so on. So, the last digit of 4^37 is 4 because 37 is an odd number.

Step 2: Consider the last digit of 256, which is 6. The last digit of 6 raised to any power is always 6.

Step 3: Subtract the last digit of (256)^38 from the last digit of (624)^37. This gives us 4 - 6 = -2.

However, since we are looking for a single digit answer, we add 10 to -2 (because there are 10 digits in a base 10 number system), which gives us 8.

So, the last digit of (624)^37 - (256)^38 is 8.