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Rules for Rational Exponents - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

The rules for multiplying and dividing exponents apply to rational exponents as well - however the operations will be slightly more complicated because of the fractions. Some basic rational exponent rules apply for standard operations. When multiplying exponents, we add them. When dividing exponents, we subtract them. When raising an exponent to an exponent, we multiply them. If the problem has root symbols, we change them into rational exponents first.

So the rules of rational exponents are the exact same as the rules of general exponents okay and why, where people mess up is they see fractions and they tend freak out and think out hell is breaking loose. But really it's exactly the same as anything else that we've talked about.
Let's look at 5 squared times 5 to the fourth. When we are multiplying our bases, all we have to do is add our exponents, so this just becomes 5 to the sixth okay? 4 to the one half times 4 to the two thirds again we're multiplying bases so all we have to do is to add our exponents. This turns into 4 to the one half plus two thirds. In order to finish this up we need to do our common denominator and combine everything but the reason why I want to show you this is the rules are exactly the same for whole number exponents as they are for fraction exponents.
Okay so what I have is on the part of the board board over here, is all the rules that we have already talked about for standard exponents okay? If we are multiplying our bases, we add our exponents. If we are dividing, we subtract power to power we multiply and negative exponent basically flips it over into the denominator. A fraction to a power that power gets distributed in. A fraction to a negative power, power gets distributed in and the negative sign flips our fraction and if we have a product to a power that power goes to both things inside okay?
The rules are exactly the same for fraction exponents as they are for normal exponents so don't let the fact that they're fractions scare you okay? Everything still holds true.

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