Question

Find unit digit of 3^81​

Answer 1

Answer:

Unit digit should be 3.

Answer 2

Given:

3^81

To Find:

Find the unit digit

Solution:

To find the value of the unit digit of any exponential with some high power that cannot be calculated easily we use the concept of cyclicity.

every digit from 1 to 9 shows some cyclicity in the case of powers which is repeated and the unit digit can be only these numbers.

In this case, we have the unit digit of base as 3, and the cyclicity of 3 is,

3= 3, 9, 7, 1

and to check the cyclicity we will express the power in the form of 4n+a

81=4*20+1

So the cyclicity is one therefore the unit digit will be 3,

Hence, the unit digit of 3^81 is 3.