Remainder problem

When 38 is divided by 3 , the remainder is 2. So, when 2 . 2 . 2 . 2 = 16 is divided by 3 , the remainder is 1 .

$\frac{38}{3}=12.667..$

here ,the remainder is 2.

so, if we square or cube this number the ratio will be same for 3.............[2 then 1 then 2 then 1] .

38 = 2 mod 3. So 38^4 = 2^4 mod 3. 2^4 = 16 . 16 mod 3 = 1