# Why is 0^0 undefined? | Summary and Q&A

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January 30, 2019
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blackpenredpen
Why is 0^0 undefined?

## TL;DR

In this video, the concept of zero to the zeroth power is discussed, with examples and explanations of different exponents and their definitions.

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### Q: What is the definition of exponents for positive whole numbers?

Exponents for positive whole numbers involve multiplying the base number by itself the specified number of times. For example, 2 to the 3rd power is calculated by multiplying 2 by itself three times, resulting in 8.

### Q: How is zero to the zeroth power defined?

Zero to the zeroth power is undefined, but a graphing exercise suggests that it can be considered equal to 1. However, this definition can lead to contradictions and inconsistencies in certain scenarios.

### Q: How are negative exponents defined?

Negative exponents are defined by following the pattern of dividing by 2 for each decrement in the exponent. For example, 2 to the negative 1 power is defined as 1/2, and 2 to the negative 2 power is defined as 1/4.

### Q: Is there a theorem that proves the value of zero to the zeroth power?

No, the value of zero to the zeroth power is not proven through a theorem. It is defined based on patterns and observations, but there can be contradictions and inconsistencies when applying this definition in certain situations.

## Summary & Key Takeaways

• The video begins by reviewing the definition of exponents and demonstrates how to calculate exponents with positive whole numbers.

• The discussion then moves on to exponents that are not positive whole numbers, such as zero and negative numbers, and the patterns and definitions that can be applied to them.

• Zero to the zeroth power is explored through a graphing exercise, which suggests that the value of zero to the zeroth power is 1.

• However, the video also points out that there can be contradictions and inconsistencies when dealing with zero to the zeroth power, leading to the conclusion that it is undefined.