is x positive or negative

Question

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.

Answer 1

To start, we can rewrite X^-2 as 1/X² . If X is a positive number, then we will have 1/(X²) 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).