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# Why is 20 to the power of 0 is equal to 1?

Updated: 9/21/2023

Wiki User

12y ago

Look at the powers of any number, but as you'd asked, let's use 20:

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20^1 = 20

20^2 = 400

20^3 = 8,000

20^4 = 160,000

20^5 = 3,200,000

....and so on.

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To get from 20^5 to 20^4 we have to divide by 8.

3,200,000 divided by 20 is 160,000. (or 20^4)

And to get from 20^4 to 20^3 we have to divide by 8 again.

160,000 divided by 20 is 8,000 (or 20^3)

The logical idea is to continue doing this.

To go from 20^3 to 20^2 we should divide 20 again.

8,000 divided by 20 is 400. (or 20^2)

To go from 20^2 to 20^1 we should divide 20 yet again.

400 divided by 20 is (you guessed it) 20. (or 20^1)

Now for the ever important one. We will continue the same formula.

To get from 20^1 to 20^0, we should divide again by 20.

20 divided by 20 is.......drumroll please.......1!!!!

So 20^0 = 20^1 / 20 = 20/20 = 1.

This works for any nonzero number. 0^0 is undefined!!!

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I know it's confusing, but it does make sense (in theory lol) Hope I helped!!!!

Wiki User

12y ago