Graduate Management Admission Test (GMAT) Practice Test

What is the value of 0 raised to the power of 0?

1. 0

2. 1

3. Undefined

4. Infinity

The correct answer is: Undefined

The value of 0 raised to the power of 0 is commonly considered to be 1 in many contexts, especially in mathematics involving combinatorics and functions. This consensus arises because defining 0^0 as 1 ensures that various mathematical expressions and theorems remain coherent and consistent. For example, in combinatorics, the number of ways to choose zero elements from a set of zero elements is naturally one way: choosing nothing. However, it is essential to recognize that 0 raised to the power of 0 can also create confusion, particularly in calculus and limits, where the behavior of functions approaching this form can yield varying results. In some mathematical contexts, 0^0 may be deemed undefined, particularly when looking at the limits of certain functions as they approach this form. Thus, while in many cases it is defined as 1, the reasoning behind viewing it as undefined arises from its inconsistency across different mathematical approaches. Understanding this debate is crucial as it reflects the nuances within mathematical principles, particularly when dealing with limits and different interpretations of function behavior.