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.
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