SOLUTION: 32x^6y^9/z^8 all under a third root sign

Question 276413: 32x^6y^9/z^8
all under a third root sign
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Simplifying a cube root involves finding perfect cubes. Since there is a denominator we will also want to rationalize the denominator. I'm going to make the denominator a perfect cube at the start. This will take care of the rationalizing denomiinator before we start. Since any exponent that is divisible by 3 is a perfect cube, all I need to do is change to :

which simplifies to:

Now we can start finding perfect cubes:

Using the properties of radicals we can separate out all the perfect cubes:

Replacing the cube roots of the perfect cubes we get:

Rearranging the factors in the numerator and combining the remaining radicals we get:

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