Question

Prove that the value of the expression: (5^18–25^8)(16^4–2^13–4^5) is divisible by 30 and 44.

Answer 1

The value of the expression is not divisible by 30 and 44.

Explanation:

$(5^1^8 - 25^8) (16^4-2^1^3-4^5)\\=(5^1^8 - 5^2^\times^8) (2^4^\times^4 - 2^1^3 - 2^2^\times^5)\\=(5^1^8 - 5^1^6)(2^1^6-2^1^3-2^1^0)\\=(5^2) ( 2^3-2^1^0)\\=(25) (8-1024)\\=(25) \times (-1016)\\= -25400$

To check the number -25400 be divisible by 30 and 44, divide the number -25400 by 30 and 44

On dividing -25400 by 30 we get, -846.66

On dividing -25400 by 44 we get, -577.27

Therefore,

The value of the expression is not divisible by 30 and 44.