Why is n^0=1? Why is any number to the zeroeth power equal to 1? I would think it would be equal to zero, since nothing multiplied by nothing is, well, I would think 0. But it is 1? Examples: (-5)^0 = 1, 0^0 = 1, 5^0 = 1

IndologietVy

IndologietVy

Answered question

2022-11-25

Why is n 0 = 1?
Why is any number to the zeroeth power equal to 1? I would think it would be equal to zero, since nothing multiplied by nothing is, well, I would think 0. But it is 1?
Examples: ( 5 ) 0 = 1; 0 0 = 1; 5 0 = 1

Answer & Explanation

Lauren Andrews

Lauren Andrews

Beginner2022-11-26Added 11 answers

Expanding on what has already been said, I want to emphasize that a 0 = 1 is a convention. There is no computation to be made, because there is no obvious meaning to "multiply with itself zero times".
The reason why the convention is reasonable is what has been mentioned by Thorben's answer and Gregory's comment: the relation a m + n = a m a n is so nice that it makes sense to extend to the rest of the integers. Once you have a 0 = 1, you also get a n a n = a n n = 1, so a n = 1 / a n
aplaya4lyfeSS1

aplaya4lyfeSS1

Beginner2022-11-27Added 2 answers

Since n k = n k + 0 = n k n 0 . This short computation suggests that n 0 should be 1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?