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Simplifying Radicals using Rational Exponents - Problem 1

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 ugly radical using fractional exponents, so what I have here is a ninth root of 7 to the 6. I don't know what 7 to the sixth is, so therefore I really don't know what the ninth root of it is, but using rational exponents would be able to make this a little bit more simple.

So whenever we take this, we rewrite our radical as a exponent so we have 7 and then when we write our exponents it's power over root, so this becomes 6 over 9. Simplifying this up 9 over 6 we can reduce divide by 3 this just ends up by going to 7 to the 2/3.

It's still not pretty, I still don't know what this is, but what I've managed to do is make my power and my root significantly smaller. This is a common statement if you want to rewrite it as a radical, we're then dealing with the cube root of 7² which is the same thing as the cube root of 49.

I still don't know what that is, but it's a lot more manageable number that 7 to the sixth, so simplifying a statement, a radical statement by using rational exponents and reducing your exponent.

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