with Mr. Potthoff
What are the numbers and how do we get them
Well, its like you start out with 1 and then keep adding the answer of the equation you just did, and the largest number you just used in the equation. So it starts out with 0, then 1, so 0 + 1 = 1. Then you get 1 + 1 = 2, then 1 + 2 = 3 and so on. Some of the first few numbers are 1, 2, 3, 5, 8, 13, 21, and so fourth.
When you use squares and numbers to add them up it comes up looking like this.
Even you have the fibonacci spiral in the palm of your hand. Literally.
This looks a lot easier then what i explained and you can actually see it for you visional learners out there.
Back to powers
So real quick, anything to the 0 power is 1. So 1 to the 0 power is 1. 4 to the 0 power is 1. 9 to the 0 power is one. Its just simple as that. Same as the 1 power. Anything to the 1 power is itself. So 4 to the power of 1 is 4, 9 to the power of 1 is 9 and so fourth.
Negative powers and Fractions
Now, this is the hard stuff. Negative powers are kind of simple but yet complicated. A negative power is the regular answer, but under 1. So 2 to the -2 power is 1 over 4 because 2 to the positive 2nd power is 4, but since its a negative you put a 1 on top of it because thats how it works. Now fraction exponents are really complicated.
Fractions are like parts of something that makes the whole number. So 8 to the 1/3 is 2. Now this is true because 2 cubed is equal to 8. Since 2 times 2 times 2 equals 8, that is the same as 3 over 3. But since its only 1 third, but 3 of them, you only need one part of what makes up that number. so 4 to the 1/2 power you need to find what times itself makes up 4. The number that does is 2, and because it was a half you only need one of the two numbers to get your answer.
Lost? So am I
Lets do some more problems.
Most of this is just knowing a lot of exponents. Like how 32 with a 1/5 power is 2, because 2 to the 5th power is 32. But 32 to the 2/5 project would be 4. Why? Because there is a 2 instead of a 1, that means you have two parts you have to multiply. Now if it were 32 to the 3/5 power it would be 8. So we already know that 2/5 is 4, but since there is another one with 3/5. you have to multiply it by 2 again and ou get 8.
This is the same thing we have been doing but what it really looks like in simplest terms. With those weird signs or "houses" it is called radical form. But thats for a different subject. From what we see we know its 16 to the 3/4 power. And we also know that 2 to the 4th power is 16. So 3 parts of 2 to the fourth power. In other words, 2 to the fourth power, or, cubed. And that equals 8.