How to Simplify Rational Exponents

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To simplify rational exponents, determine the common denominator for the exponent fractions, add the fractions together and multiply the bases. Solve a math problem with rational exponents using instructions from a math teacher in this free video math lesson.

Part of the Video Series: Math Problems & History
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Video Transcript

Ooo, how do you simplify a rational exponent and stuff? That's like disgusting and stuff. Hi I'm Jimmy and I'm here to show you how to simplify rational exponents. Now every time you see the word rational that implies fractions and so fractions aren't the most pleasant to deal with in the world but as long as you know your fractions you will be o'kay. So here is a quick example for you. Suppose you want to simplify X 1/4 to X 1/2. Now because you are multiplying the same base with different exponents you are actually going to be adding the 2 so your job is to find out what 1/4 1/2 is. Now because they are unlike fractions you basically have to treat this as a standard adding fraction problem so what you do as long as you are comfortable with the fraction mathematics just find the least common denominator of 4 and 2 which as you know is 4. Now the first fraction, the first denominator stays the same so that means the first numerator stays the same as well. Now the 2 though has to multiply by 2 to give me 4 so after I multiply the bottom by 2 I multiply the top by 2. So 2 X 2 is 4 and 1 X4 has to give me 2 as well. Now adding these two together 1/4 2/4 is going to give me 3/4 so that means at the very very end next to the X 1/4 x X 1/2 is going to give me X to the 3/4 power. Now if they give you fractions with the same denominators that is even better so here is a brief illustration of that. Suppose you have X 3/5 over X 1/5. Now if they are right on top of each other with the same base you can subtract the exponents because the same denominator it is even better so you will have X 3/5 - 1/5. Now because you know 3/5 - 1/5 is 2/5 that is going to be your final result. So I'm Jimmy and this has a glimpse on how to simplify rational exponents.


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