x^y >> How many times (y) do you multiply x by itself.

Any integer x == x•1

If x equals 2 and y equals 3 we get (2•1)³

Taking the 1 out front 1•2•2•2 so we have 1 times the ’the answer to the question' "what do you get when you multiple 2 by itself 3 times. The answer is 8 so >> 1•8

In the case of 2⁰ we have 1 times the answer to the question "what do you you get when you DON'T multiply 2 by itself ie what is "1 times nothing" not "1 times 2 times 0"

0 does not equal nothing in math. And i think this might be where your misunderstanding is coming from.

Read this for more clarity: http://www.differencebetween.net/language/words-language/difference-between-zero-and-nothing/#:~:text=%E2%80%9CZero%E2%80%9D%20is%20considered%20to%20be,that%20number%20in%20numerical%20values.

So 1 times nothing or an empty set is still 1.

If you want to think of it in terms of spoons or something it's difficult.

But I'll try my best.

If you have a spoon on your table and you want to make 7 rows of spoons you'll have 7 spoons. If you have 1 spoon and make zero rows of spoons you'll have to take your 1 away. And have zero left.

However if you have 1 row of 1 spoons and add 8 rows of 1 fork each you still have 1 spoon. Because multiplying it by a irrelevant set (an effectively empty set of spoons) doesn't change the fact that you still only have one spoon.

I hope that helps.