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# Simplifying Radicals using Rational Exponents - Problem 1

###### 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 7Â² 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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###### Carl Horowitz

B.S. in Mathematics University of Michigan

He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his step-by-step explanations are easy to follow.

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