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

Answers 1

Answer:

The unit digit of [tex] {4}^{2021} [/tex]is 4.

Step-by-step explanation:

Here given term,

[tex] {4}^{2021} [/tex]

We want to find unit digit of [tex] {4}^{2021} [/tex]

Calculation of [tex] {4}^{2021} [/tex]is not possible.

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

Let,power of 4 be x

I.e,[tex] {4}^{x} [/tex]

When x is odd,

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

So,

[tex] {4}^{1} = 4 \\ {4}^{3} = 64 \\ {4}^{5} = 1024 [/tex]

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,

[tex] {4}^{2} = 16 \\ {4}^{4} = 256 \\ {4}^{6} = 1096[/tex]

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

Here given [tex] {4}^{2021} [/tex]

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 [tex] {4}^{2021} [/tex]is 4.

Know more about unit digit,

1) https://brainly.in/question/500242

2) https://brainly.in/question/16772489

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