What is the value of x^0 for any non-zero number x?

The value of x^0 for any non-zero number x is defined as 1. This is based on the properties of exponents. The zero exponent rule states that any non-zero number raised to the power of zero equals one.

To understand why this is the case, consider the pattern of decreasing the exponent by one. For example, if you have x^3 = x * x * x, then x^2 = x * x, and continuing this pattern leads to x^1 = x. When you further decrease the exponent to zero, you can think of it in terms of division: x^1 divided by x^1 gives you x^(1-1) or x^0. Since x^1 = x, dividing it by itself (as long as x is not zero) results in 1, therefore x^0 = 1.

This property holds true for all non-zero values of x, ensuring that x^0 is universally defined as 1, while the other choices do not align with the established rules of exponents.