Graduate Management Admission Test (GMAT) Practice Test

What is the result of any non-zero number raised to the power of zero?

1. Undefined

2. 1

3. 0

4. It varies

The correct answer is: 1

When any non-zero number is raised to the power of zero, the result is always 1. This principle is rooted in the rules of exponents. To understand why this is the case, consider the property of exponents that states when you divide two like bases, you subtract the exponents. For example, if you have a number \( a \) (where \( a \) is non-zero) and you look at the expression \( a^n / a^n \), which simplifies to \( a^{n-n} \). Since any non-zero number divided by itself equals 1, this means \( a^n / a^n = 1 \). Therefore, we conclude that \( a^{n-n} = a^0 \), leading to \( a^0 = 1 \). This concept applies universally to all non-zero numbers, providing a consistent outcome that reinforces the understanding of exponent rules. Hence, the correct answer is that any non-zero number raised to the power of zero equals 1.