ELI5, how does 2^0 power equal 1?

Question

I’m doing my GED and passed that math part but this never came up. I saw it on a meme and am lost.
Help!!??

In: 9770

Answer 1

Powers are repeated multiplication.

So 2^1 = 2

2^2 = 2×2 = 4

2^3 = 2x2x2 = 8

2^4 = 2x2x2x2 = 16

If you look at the list above, but go backwards, you see that when I reduce the power, I multiply by 2 one fewer time. Equivalently, I divide by 2, or halve the number.

2^0 would be the next term in this sequence, and would be half of 2^1.

2^1=2, so 2^0 is half of that, 1.

We can go even further into negative powers, which is now explicitly dividing.

So 2^-1 = 1/2

and 2^-2 = 1/4.

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If you are worried about how ‘repeated multiplcation’, starts at 1, note that multiplcation by 1 makes no difference, so it is therefore the starting point for any multiplcation.

That is, I started earlier with 2^1 = 2.

We can multiply by 1, and this makes no difference, so

2^1 = 1×2

So by ‘repeated multiplcation’, we really mean ‘repeated multiplication *starting at 1*’, that is why 2^0=1, since we start with 1 and then do nothing to it.