Concept: The question tests on the basics of Exponents in a DS format


First of all (4x)^(5−3x)=4^x(5−3x)

For this expression to be equal to 1, x(5−3x) must be equal to 0.


 --> x=0

or x=5/3

So basically the question asks whether x=0 or x=5/3.

(1) x is an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Insufficient.

(2) x y ≠x, hence x is not equal to 0. But x can be any other number, integer or not integer. Insufficient.

(1)+(2) x is an integer but not 0. So, x is not 0, not 5/3. Hence x(5−3x)≠0, hence (4^x)^(5−3x) does not equal to 1. Sufficient.

(option C)