Answer:
B) 4
Step-by-step explanation:
We can solve this by observing some pattern.
The powers ending in 4 as unit digit are:
[tex] {8}^{2} , {8}^{6} , {8}^{10} , {8}^{14} , {8}^{20} ,...[/tex]
The exponents form the sequence:
2,6,10,14,20,...
We need to check if 62 belongs to this sequence.
This is an arithmetic sequence with a common difference of 4 and a first term of 2.
The explicit formula is
[tex]2 + 4(n - 1)[/tex]
We equate this to 62 and solve for n.
[tex]2 + 4(n - 1) = 62 \\ 4(n - 1) = 60 \\ n - 1 = 15 \\ n = 16[/tex]
Since n is a natural number, 62 belongs to the sequence.
Hence
[tex] {8}^{62} [/tex]
will have a unit digit of 4.
