Question

Which is the digit in the unit place of 3²⁰¹⁶ *​

Answer 1

Answer:

The best trick to solve this question is to run a check over units place first.

3^1= 3

3^2=9

3^3=27

3^4=81

3^5=243

3^6=729

3^7=2187

3^8=6561

3^9=19683

3^10=59049

Um, is it just me or you too did notice something there?

Unit place begins to repeat itself after every 4th time.

Unit place in 3^1 is same as unit place in 3^5.

3 and 243.

Thus, we can conclude that if higher power is divided by 4, the remainder will tell us which smallest power of 3 will share the same unit place's digit as that of big number.

So, 2016÷4=504 and remainder 0.

Thus, 3^2016 will have the same digit at its unit place as that of 3^4.

Thus, our answer is 1.