If x is a nonzero real number, is x^{-2} always positive, always negative, or positive or negative depending on whether x is positive or negative? explain answer.
To start, we can rewrite X^{-2} as 1/X^{2} . If X is a positive number, then we will have 1/(X^{2}) which is just a positive fraction. If X is a negative number, then we will have 1/( -X * -X). Since the product of two negative
numbers is a positive number: 1/( -X * -X) = 1/(X2) which is just a positive fraction. So it doesn't matter whether X is positive or negative, X^{-2} will always be positive (when X is a nonzero real number).