This is a pattern problem. If 41 is raised to the power of 33, the unit digits will remain 1 for any power. 41^1 = 41' 41 ^2 =.....1, 41^10 = .....1
For 43 , the pattern for the power will be 43^1= 43, 43 ^ 2 = ....9, power 3 units digit 7 from 27, power 4 unit digit = 1. From this, the pattern is 3,9,7,1,3,9,7,1. The pattern repeats itself every 4th power. Therefore, 43^32 will have 1 as a unit digit since 32 is a multiple of 4 while 43^33 will have a unit digit of 3 and not 7.

For the last option 47, the pattern is 7,9,3 and 1 and this repeats itself every 4th power. Therefore, 43^32 has 1 has unit digit while 43^33 has 7 has unit digit.

The answer is option III only.

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