Question

Units digit of the number
`2^(4000)`

Answer 1

6

Explanation:

We want to find the units digit of
`2^(4000)`. Let's first look for a pattern:

`2^(1)=2`

`2^(2)=4`

`2^(3)=8`

`2^(4)=16`

`2^(5)=32`

`2^(6)=64`

`2^(7)=128`

`2^(8)=256`

...and so on

Notice the units digits: 2, 4, 8, 6, 2, 4, 8, 6, ... It repeats every four!

This means that for every exponent of 2 that is a multiple of 4 (like 4000 in the problem), the units digit will always be the fourth number in the repeating pattern: 6.

The answer is thus 6.

~ an aesthetics lover