The remainder , when (2222⁵⁵⁵⁵ + 5555²²²²) is divided by 7, is

Explanation:-

aⁿ + bⁿ is always divisible by (a + b) when n is odd.
So,
(2222⁵⁵⁵⁵ + 5555²²²²) is always divisible by (2222 + 5555) = 7777
And 7777 is multiple of 7,
so (2222⁵⁵⁵⁵ + 5555²²²²) is divisible by 7