SOLUTION: Please help, I am soooo lost with 2 problems: 1: Cube Root of 270x divided by cube root of 10xy^2 2: Cube root of x^2 divided by cube root of 4 Thank you so much!

Question 398823: Please help, I am soooo lost with 2 problems:
1: Cube Root of 270x divided by cube root of 10xy^2
2: Cube root of x^2 divided by cube root of 4
Thank you so much!
Found 2 solutions by josmiceli, jsmallt9:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

----------------------------------------------------------

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
With expressions like these, a radical over the same kind of radical, I like to use the following procedure:
Use the property to combine the two radicals into a single radical.
Reduce the fraction inside the radical, if possible.
If the denominator is not a perfect power of the type of radical, then multiply the numerator and denominator by some expression so that the denominator becomes a perfect power of the type of radical.
Use the same property as step 1, only in reverse, to split the radical back to a radical over a radical.
Simplify. If the previous steps were done correctly, there should be no radicals remaining in the denominator.

Let's see this in action.

1) Combine radicals:

2) Reduce the fraction inside. The x's cancel and a factor of 10 cancels leaving:

3) If the denominator is is not a perfect power of the type of radcial, then multiply the numerator and denominator by whatever makes the denominator a perfect power of the type of radical. Since we are working with cube roots, we are looking to make the denominator a perfect cube. All we need is another factor of y:

which simplifies to:

4) Split the radical:

5. Simplify.

Since there are no perfect cube factors in 17y, the radical in the numerator will not simplify further.

1. Combine the radicals:

2. Reduce the fraction. This fraction will not reduce.
3. Make the denominator a power of the type of radical. The "nearest" perfect cube to 4 is 8. So we just have to multiply the numerator and denominator by 2:

which simplifies to:

4. Split the radical:

5. Simplify.

There are no perfect cube factors in so the numerator will no simplify any further.

Note 1: The procedure I've described is not the only way to simplify your expressions. But it is pretty efficient at handing radical over radical expression.
Note 2: Any procedure used correctly should simplify your expressions to the same results as we got above.
Note 3: If the radicals are of different types then use fractional exponents to make them the same type. For example:

Now that the radicals are both 6th roots, we can use the procedure above:
1. Combine:

2. Reduce. This will not reduce.
3. Make the denominator a power of the type of radical:

4. Split

5. Simplify. Since sixth roots are supposed to be positive and since we do not know if y is positive, we should use absolute value when simplifying :

RELATED QUESTIONS
cube root of 2 divided by cube root of... (answered by stanbon)
i need help in finding the cube root of 16x^5 divided by the cube root of... (answered by Fombitz)
cube root of... (answered by richwmiller)
cube root of 2(cube root of 4 subtract 2 times the cube root of... (answered by jsmallt9)
The cube root of x-1 = the cube root of x^2+ 2x... (answered by mbarugel)
1 over cube root of... (answered by rothauserc)
the value of 2 cube root 4 + 7 cube root 32 - cube root 500... (answered by mananth)
(cube root of 3-square root of 2)(cube root of 3+square root of 2)=? (answered by Fombitz,ikleyn)
can you help me simplify this radical expression? the problem is cube root of 16x^4y,... (answered by Boreal,solver91311)