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### Interview Answer

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Ripped open by metal explosion. And any number to the first power is just going to be equal to that number. And then we can go from there, and you will, of course, see the pattern.

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If we say what 2 squared is, well, based on this definition, we start with a 1, and we multiply it by 2 two times. So times 2 times 2 is going to be equal to 4. And we've seen this before. You go to 2 to the third, you start with the 1, and then multiply it by 2 three times.

So times 2 times 2 times 2. This is going to give us positive 8.

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And you probably see a pattern here. Every time we multiply by or every time, I should say, we raise 2 to one more power, we are multiplying by 2.

Notice this, to go from 2 to the 0 to 2 to the 1, we multiplied by 2. I'll use a little x for the multiplication symbol now, a little cross. And then to go from 2 to the first power to 2 to the second power, we multiply by 2 and multiply by 2 again. And that makes complete sense because this is literally telling us how many times are we going to take this number and-- how many times are we going take 1 and multiply it by this number?

And so when you go from 2 to the second power to 2 to the third, you're multiplying by 2 one more time. And this is another intuition of why something to the 0 power is equal to 1.

## Galt MacDermot:3-5-0-0 Lyrics

If you were to go backwards, if, say, we didn't know what 2 to the 0 power is and we were just trying to figure out what would make sense, well, when we go from 2 to the third power to 2 to the second, we'd be dividing by 2. We're going from 8 to 4. Then we'd divide by 2 again to go from 2 to the second to 2 to the first. And then it seems like we should just divide by 2 again from going from 2 to the first to 2 to the 0.

And that would give us 1.