What happens if the exponent is 1

Let's start out with a couple simple examples. The general case works the same way. We just need to keep track of the number of factors we have. This rule results from canceling common factors in the numerator and denominator.

We can raise exponential to another power, or take a power of a power. We really have no choice. Barry 2, 10 10 silver badges 19 19 bronze badges.

On the one hand, extreme redundancy As an unrelated tangent, newer versions of MathJax make root symbols so much more beautiful than they were in the past. Add a comment. Stefan Perko Stefan Perko One has to be clear what one is dealing with! I totally forgot what the original question was! John John Start with the natural numbers, define a starting point and the notion of a successor.

Daniel R. Collins Daniel R. Collins 7, 1 1 gold badge 19 19 silver badges 38 38 bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post.

Linked 4. Related 9. So 2 is going to be we're only going to multiply it by the 2. I'll use this for multiplication. I'll use the dot. We're only going to multiply it by 2 one time. So 1 times 2, well, that's clearly just going to be equal to 2. 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. 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. 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.

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.