ANSWERS: 3

i'll give an example to help explain why, using the number 8 8^1 = 8 8^2 = 64 8^3 = 512 To get from 8^3 to 8^2 we have to divide by 8. And to get from 8^2 to 8^1 we have to divide by 8 again. if you continue..... to go from 8^1 to 8^0 we should divide by 8. So 8^0 = 8^1/8 = 8/8 = 1. This works for any nonzero number. 0^0 is undefined.

because it makes one wish become true

Here's the way we were taught it in school. If you multiply two different powers of the same number, e.g. 2 to the power 2 and 2 to the power 3, the product is the same as 2 raised to the power of (2 + 3). For example, 2 to the power 2 is 4, and 2 to the power 3 is 8, and if you multiply 4 by 8, you get 32. That's the same as 2 raised to the power 5. The reason why something raised to the power zero is equal to one is to make this convention consistent. So, 2 to the power 2 multipled by 2 to the power zero should be equivalent to 2 to the power (2 + 0). This implies that raising a number to the power zero is equal to one. Apologies if this is hard to understand, but it's hard to put into words.
Copyright 2020, Wired Ivy, LLC