Why does every number raised to the power of zero equal one?

PFirst of all, we have to pay attention to the following: That rule is not valid for all the numbers! It is only valid for numbers that are different from zero, since `0^0` results in indeterminacy (the result cannot be determined).

After this explanation, and before answering the question, I will remember you that in every fraction, when the numerator is equal to the denominator, the result equals 1 (one). So, `a^m/a^m=1`.

Here we have another important rule that allows us to divide powers with the same basis: `a^m/a^n=a^(m-n)`. This rule tells us that when we divide powers having the same basis we can simplify them by keeping the same basis and subtracting the exponents.

Finally, we will answer to the question. So, if we have, for instance `2^5/2^5`, its result will be one if we apply the first rule, since the numerator is equal to the denominator. If we had chosen the second rule, the result would have been `2^5/2^5 = 2^(5-5) = 2^0`. It is obvious that no matter what rule is used, we have to reach the same value and it means that `2^0=1`.

In conclusion, every power having a 0 exponent, and whose base is different from 0, results in one.

Check out our List of Questions to get to know a little more about the most diverse topics related to mathematics. If you have any pertinent (math) question whose answer can not easily be found, send us an email on the Contact page with the question. We will be happy to respond. In the event that you detect any errors in our answers, do not hesitate to contact us!