Question

How do you simplify `root3 (x^6 y^7)/root3 9`?

Answer 1

`root(3)(x^6y^7)/root(3)9` can be written as =`(xy)^2root(3)(y/9)`

Explanation:

You have the expression `root(3)(x^6y^7)/root(3)9`
Remember that the cubic root `root(3)` of something means a number which multiplied with itself three times `(z*z*z)` gives the number under the root sign.

("multiplied with itself three times" is, of course, not quite precise, but I mean that n is a factor three times, i.e. `z*z*z`.)

Let's rewrite the expression a little:

`root(3)(x^6y^7)/root(3)9 = root(3)((xy)^6y/3^2)`
=`(xy)^2root(3)(y/3^2)`
Or if you will
=`(xy)^2root(3)(y/9)`
depending on what you prefer.

We may be fooled to think that `root(3)9` can be simplified, but it is not a cubic number. If we had had `27=3^3` instead, we would get the nice expression
=`(xy)^2/3root(3)(y)`