expression 2222 to the power 7777 + 7777 to the power 2222 is divisible by .
Answers
Given : 2222⁷⁷⁷⁷ + 7777²²²² (2222 to the power 7777 + 7777 to the power 2222)
To find : 2222⁷⁷⁷⁷ + 7777²²²² is divisible by
Solution:
2222⁷⁷⁷⁷ + 7777²²²²
= (1111 * 2) ⁷⁷⁷⁷ + (1111*7)²²²²
Concept used (ab)ⁿ = aⁿᵇⁿ
= 1111 ⁷⁷⁷⁷ * 2 ⁷⁷⁷⁷ + 1111²²²² * 7²²²²
= 1111 ²²²²⁺⁵⁵⁵⁵ * 2 ⁷⁷⁷⁷ + 1111²²²² * 7²²²²
Concept used aⁿ⁺ˣ = aⁿ * aˣ
= 1111 ²²²² * 11⁵⁵⁵⁵ * 2 ⁷⁷⁷⁷ + 1111²²²² * 7²²²²
Taking 1111 ²²²² as common
= (1111) ²²²² ( 1111⁵⁵⁵⁵ * 2⁷⁷⁷⁷ + 7²²²²)
hence divisible by (1111) ²²²²
Hence 2222⁷⁷⁷⁷ + 7777²²²² is Divisible by (1111) ²²²²
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