In the expansion of (x^2 + x^(-2))^22, how many terms are there where x has a negative exponent?
Your expression is written like this: (x^2 + 1/x^2)^22 . So both terms are +. Therefore, there is NO minus sign in the expansion of the 23 terms.
Now, for negative EXPONENTS, I counted 11 of them from x^-44, x^-40, x^-36.........x^-4.