What does \(10^0\) equal?

The expression (10^0) equals 1 based on the rules of exponents. In mathematics, any non-zero number raised to the power of zero is defined to be 1. This rule applies regardless of the base, as long as the base is not zero.

The reason this rule holds can be understood through the properties of exponents. For example, when you divide two powers with the same base, you subtract the exponents: (a^m / a^n = a^{m-n}). If both powers are equal, such as (10^1 / 10^1), this simplifies to (10^{1-1} = 10^0). Since (10^1 / 10^1) is equal to 1, it follows that (10^0) must also equal 1 to maintain the consistency of the exponent rules.

Understanding this concept allows students to apply the property to other exponential expressions, fostering a deeper comprehension of how exponents work in various mathematical contexts.