How to Divide Exponents

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Exponents, like any other number, can be divided in order to be simplified. Properly divide exponents with helpful instruction from a mathematics instructor in this free video on learning math.

Part of the Video Series: Mathematics: Exponents
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Video Transcript

Hi, I'm Jimmy Chang. I'm an expert from Saint Petersburg, Florida. And we are here to talk about to divide exponents. What you need for this exercise are a pen or pencil, piece of paper, and a calculator if you would like to use it. Now, dividing exponents revolves around one very fundamental rule. So, we'll go over a few examples on that rule, very soon, as in now. Now, the one rule that we'll be using primarily is of this particular one. B to the m over b to the n is equal to b to the m minus n. What the means here is if you have two numbers as in, but using the same base that's the very critical part; if you have a base raised to a power divided by the base of another power. When you want to combine those exponents when you're dividing, you're actually subtracting them. So, in other words, division of these is actually associated with subtraction. So, hypothetically, if you want to use this rule, you get x to the seventh, divided by x to the fourth. Now, remember if this was y to the fourth, you can't do it. The bases have to match. Then you would do x to the seventh minus four, which would be x to the third power. Now, similarly, if you have x to the tenth, over x to the eleventh, division there, again making sure the bases match, you have x to the ten minus eleven. Which is going to be x to the negative one power. Now, if you already know the negative exponent rule, as you might imagine, if you have a negative exponent here, you can move it down to what becomes a positive exponent. And that's an example of a negative exponent rule. So, in a sense we're kind of, and this example uses two rules at once, if you want your final answer in positive exponent form. And lastly if you have something, let's just use something a little more quirky, if you have x to the 5.2 over x to the 3.1, decimals, well you still have the same idea. Go ahead and subtract the exponents. You have x to the 5.2 minus 3.1. So, the 5.2 minus 3.1 is going to give you 2.1. So, what you have here as a result, is x to the 2.1. So, as you can tell, it's a pretty straight forward rule to use as long as you're consistent about it and making sure that the bases match. so, I'm Jimmy Chang and that's how you divide exponents.

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