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Lesson 5: Exponents with negative bases

# The 0 & 1st power

Different ways of thinking about exponents. Raising a number to an exponent means multiplying that number by itself a certain number of times. Any non-zero number raised to the zero power will be equal to one, and that any number raised to the first power will be equal to itself. Created by Sal Khan.

## Want to join the conversation?

• how do you type the multiplication symbol on a keyboard?
• Well, there are two ways that I know of:
- An asterix = * (which, by the way, is from a Greek root word that means "little star") You can usually find it where your numbers are on your keyboard. Ex: 12 * 6 = 72
- A lower case X = x. I don't think I have to tell you where that is on a keyboard! Ex: 12 x 8 = 96
Also as a footnote to this, "x" will sometimes not work because it could also represent a variable. So be careful!
Hope this helps! :)
• Why any number (except 0 ) raise to power 0 is always 1 ?
• It has to do with the properties of exponents.
Here's a good example:
Lets say you have a number a^x/a^y and x = y.
Using a property of exponents you can rewrite the equation as a^(x-y) and since x=y that becomes a^0.
Also since x = y, a^x = a^y and so it becomes 1/1 or just 1.
• At Sal says it will make sense. I never really got past the 2 to the 0 power. I don't understand how he took two, put a zero above it, and then turned it into a one?! How does that work?
• What he showed helped me understand why it does that, so now let me try to explain it for you:
He changed the way he did the exponents to multiplying `1 times` how many numbers (the number that the exponent is) to that one.

So when it is `2⁰ = 1` because there aren't any `2`s to multiply by.
So something as big as `1,000,000⁰ = 1`

Now let's do it regular:
When you have `4⁶ = 1 × 4 × 4 × 4 × 4 × 4 × 4 = 4096`
Well, that is a bit too big of a number so let's do `3² = 1 × 3 × 3 = 9`

• What does the little circle above the 2 mean?
• The circle above is the exponent. The rule is that any number raised to the power of 0 equals to 1. So if 2 or 1,000,000 is raised to the power of 0 it equals 1.
• Why incorporate the 1 at all?
• Because incorporating the 1 helps to give more intuition for why every number raised to the power of 0 equals 1. Sure, you can divide 2 by 2 to get 1, however, you can also say "hey, I have no 2's, but still have the 1."
• math isnt mathing anymore.
• bruh I understood it for a hot second than you hade to do THIS
• () I really don't understand how any non-zero number to the power of 0 is 1.
• because your not multiplying it by itself any times
• I understood it but now I don’t