What Is a Zero Exponent?

Essentially, an exponent that is zero is equal to a variable to the power of an exponent times a variable to the negative power of the same exponent. For instance, x² times x^-2 is equal to x² divided by x^-2. Any number divided by itself is equal to one.

Zero to the power of zero is a special case, however. Some mathematicians say that it equals one, while others say that it equals zero.