Contributor: Briana Pincherri. Lesson ID: 11245
You may have had a "negative" experience with exponents, with "zero" desire to learn them. Watch these simple videos and try some easy examples, and you'll become an exponent of using . . . exponents!
Let's find out!
At this point, you should be familiar with the terms base and exponent.
Remember that the base is the number you will be multiplying by itself, and the exponent is the little ^{tiny} number that tells you how many times you will multiply the base by itself.
Let's take a look at this video, What Do You Do With a Zero Exponent? Virtual Nerds: Real Help:
As you saw, any number to the 0 power is 1. It doesn't matter if it is x^{0}, 4^{0}, or even 1,000,0001^{0}. Each of these will be equal to 1!
Great! We now know how to handle positive exponents and exponents of 0.
When we have a negative exponent, we want to do the inverse (or opposite). Typically, when we see an exponent, we know we are going to be multiplying.
It's division. The negative exponent simply tells us how many times to divide by the base.
While it may sound tricky, I think you will like it. You are about to see that the negative exponent just means you are going to:
I have a feeling it will make more sense by looking at the example:
2^{3} = 
Now think, what would the positive exponent look like? 
2^{3} = 
Well, it would look like this! Now, take the reciprocal and you are finished. 
2^{3} = 
1 

2^{3} 
As you can see in this example, when you have negative exponents, you simply find the reciprocal and include the positive version of the exponent.
In the answer above, you can now do the math to find the final answer to be ^{1}/_{8} (because 2 x 2 x 2 = 8).
Here are a few more examples to take a look at:
5^{3} 
= 
1 
= 
1 

5^{3} 
125 
11^{2} 
= 
1 
= 
1 

11^{2} 
121 
3^{4} 
= 
1 
= 
1 

3^{4} 
81 
5^{2} 
= 
6 
= 
6 

6 
5^{2} 
25 
You can feel free to look back at these examples at any point as a guide.
Remember, when dealing with negative exponents, you can simply decide what the positive version of the exponent would be and use it in the reciprocal.
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