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### Course: Get ready for Algebra 1>Unit 5

Lesson 3: 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
• It might take a while for it to fully 'sink in' to your brain. Perhaps try reviewing the video a couple of times to see if it gets any clearer.
Hope this helps!
-Catlovertheaspiringvet🩺🐈
(1 vote)
• Please help. I don't understand how you get 1 for the answer wouldn't be 2 since you aren't multiplying it by itself?
• Not quite, you see we multiply an exponent by whatever number is in that position ,so if zero is in the position The number multiplies itself zero times ,And that number is just zero . But since there is an invisible one beside the number ,That makes the answer one instead of zero.