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

**Solution**

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∗(5−3x)=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)**