How to Use Properties of Rational Exponents

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Using the properties of rational exponents can allow you to perform complicated math equations more easily. Find just what these properties are and how to use them with help from a math expert in this free video.

Part of the Video Series: Exponents
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Video Transcript

Hi, I'm Jimmy Chang. I'm a Math Expert from St. Petersburg, Florida, and we're here to talk about how to use properties of rational exponents. What you'll need for this exercise are a pen or pencil, piece of paper and a calculator, scientific or graphing, whichever is, is appropriate or what you have. Now, properties of rational exponents actually follow all the properties of ordinary exponents. In other words, the properties of exponents apply to all exponents, rational or not. So, we're going to go over a few examples on these properties and so, here we go. Now, one property of exponents that you want to be aware of and to review is that to use the property successfully you need to be sure that the bases match. In other words, if you have b to the m times b to the n, make sure that the bases match and if they do match, you can add those exponents together. Now, just as a friendly reminder, the rational exponents tend to be in fraction form. So, if you have something like for example, b to the one half times b to the one half. Since you know that the bases do match, what you do is you add those. So, as might imagine, one half plus one half is b to the one or we simply right the letter b. Now, another property would be, if you have base to a power divided by base, the same base to another power, you would subtract those exponents as long as the bases match, which they do here. X to the one third divided by x to the one fourth; now, you would subtract those, you'll have x to the one third minus one fourth. Now, to subtract these of course, you need to find the least common denominator and in this case, it happens to be twelve. So, you have x to the three twelfths, four twelfths, minus three twelfths. Now again, all of these is in your exponent form and so four twelfths minus three twelfths is going to give you x to the one twelfth. Now, one last major exponent property is if you have b to the power raise to another power. What you do with those exponents is you would multiply those exponents together. So, it would be b to the m times n. Notice because there's only one base, you only worry about the one base, not two. So, for example if you have, let's just say, three to the one half raise to the one fourth. What you do is you multiply the one half and the one fourth, like so and in this case, as you know with multiplication of fractions, you multiply across. One times one is one and two times four is going to be eight. So, three to the one half to the one fourth is really three to the one eighth. Now, there are many other properties of exponents that you apply; but these are some of the major ones. And so, I'm Jimmy Chang, and that's how to use properties of rational exponents.


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