Question

How do you simplify `root3(y^6)/(root3(27y)*root3(y^11))`?

Answer 1

`1/(3y^2)`

Explanation:

Because all the terms are cube rooted (and the expression contains no addition or subtraction), the cube root can be moved to the outside of the expression: `root3(y^6/(27y.y^11))`

We can simplify the denominator using the fact that `a^n.a^m=a^(n+m)`
Both terms in the denominator are `y` raised to a power, so when we multiply them we add the indices to get:

`root3(y^6/(27y^12))`

We can now divide the top and the bottom of the fraction by `y^6` giving us `1` in the numerator, as `y^6/y^6=1`

For the denominator we use `a^n/a^m=a^(n-m)` to get: `27y^12/y^6=27y^(12-6)=27y^6`

So the expression becomes: `root3(1/(27y^6))`

The cube root of `27` is `3`.

`root3(x)` is equivalent to `x^(1/3)`, so `root3(y^6)=y^(6/3)=y^2`

Therefore the expression fully simplifies to: `1/(3y^2)`