Why does 7 to the 0 power equal 1?

Answer 1

Look at the powers of any number, but as you'd asked, let's use 7:

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7^1 = 7

7^2 = 49

7^3 = 343

7^4 = 2,401

7^5 = 16,807

....and so on.

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To get from 7^5 to 7^4 we have to divide by 7.

16,807 divided by 7 is 2,401. (or 7^4)

And to get from 7^4 to 7^3 we have to divide by 7 again.

2,401 divided by 7 is 343 (or 7^3)

The logical idea is to continue doing this.

To go from 7^3 to 7^2 we should divide 7 again.

343 divided by 7 is 49. (or 7^2)

To go from 7^2 to 7^1 we should divide 7 yet again.

49 divided by 7 is (you guessed it) 7. (or 7^1)

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

To get from 7^1 to 7^0, we should divide again by 7.

7 divided by 7 is.......drumroll please.......1!!!! (or 7^0!!!)

So 7^0 = 7^1 / 7 = 7/7 = 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!!!!