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

1 Answer
Feb 22, 2017

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)