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Rules for Rational Exponents - Problem 4

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!

Simplifying an expression with rational exponents. So behind me I have a problem that is a problem with a bunch of square root. We're trying to simplify it. The first thing I always do whenever I see a problem like this, is to rewrite these radicals as exponents. I'm a lot more comfortable dealing with exponents than radicals.

So I'm taking this, and write it into exponents. The fifth is our power. The sixth is our root, we go to power over root. So this becomes x to the 5/6. X the power is 1, so this is just going to be 1 over 6. Here our power over root is going to be 7 over 6.

So now that we have this rewritten as exponents, we know what our rules of exponents are. When we are multiplying bases we just add our exponents together. Think about x² times x³, you multiply, you add your exponents. Same exact thing times in here.

So here x to the 5/6 times x to the 1/6 just becomes x to the 6/6, which is x to the first. X to the 5/6 times x to the 7/6, again adding our exponents we get x to the 12/6. 12/6 is 2, so this ends up being x².

So we were able to simplify this expression with a bunch of square root by rewriting our square roots as exponents, and then using our laws of exponents to simplify.

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