Question

What is the unit digit of 4^(2021)?

Answer 1

Answer:

The unit digit of ${4}^{2021}$is 4.

Step-by-step explanation:

Here given term,

${4}^{2021}$

We want to find unit digit of ${4}^{2021}$

Calculation of ${4}^{2021}$is not possible.

So by a short trick ,we can solve this problem.

Let,power of 4 be x

I.e,${4}^{x}$

When x is odd,

For example x=1,3,5,......

So,

${4}^{1} = 4 \\ {4}^{3} = 64 \\ {4}^{5} = 1024$

So it is clear that when power of 4 is an odd number,unit digit will be always 4.

When x is even,

For example x=2,4,6,......

So,

${4}^{2} = 16 \\ {4}^{4} = 256 \\ {4}^{6} = 1096$

When power of 4 is an even number, unit digit will be always 6.

Here given ${4}^{2021}$

Power of 4 is 2021 which is an odd number.

It is prove that when power of 4 is an odd number,unit digit will be 4.

So,we can say the unit digit of ${4}^{2021}$is 4.

Know more about unit digit,

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