Why do you think D is correct ? I think you're assuming x is an integer, right ? We can't assume so unless explicitly stated. For example :
If x = 1, then 7^7/7^x is an integer, else not
(2) |x| = x^2 only if x = 0 or 1 or -1
In which case the expression is an integer, so answer is B.
Yes, you are correct. I was assuming x to be an integer. Thanks for pointing that out.