Simplifying Radicals using Rational Exponents - Problem 1


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.

higher index radical rational exponent