Given that x must be a negative number,

Quantity A will yield a negative number because a negative number raised to an even power will be positive, and A is the opposite of that number, which is negative.

and

Quantity B will yield a positive number because a negative number raised to an odd power will be negative, and B is the opposite of that number, which is positive.

E.g., if x = -11:
Quantity A = $- \frac{1}{-11*-11*-11*-11} = -\frac{1}{121*121} = -\frac{1}{14641}$
Quantity B = $- \frac{1}{-11*-11*-11} = -\frac{1}{-11*121} = \frac{1}{1331}$