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Why does a^0 equal to 1?

something I was really curious about

#math 1 min read

This is silly. Everybody knows a0=1. But why?

I didn't know the answer to this question. And that's very dumb. I kept questioning because it didn't make sense to me:

"When we multiply something with 0, it equals to 0, right? Doesn't a0 mean that there are 0 a?"

And all sort of things, which do not make sense.

But I finally knew the logical and algebraic answer.


We'll need to understand a law of exponent first:

am+n=aman

Now that we understand, let's prove that a0=1

Proof

Proof

Well, I gotta learn how to write LaTeX efficiently. Until then, consider doing a handwriting recognition course.


This was a very simple thing, but I wanted to share it.

Alright, happy solving!


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