Write a quotient of two cube roots so that the answer when simplified is 3a^2/4b^3?

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One way to do this would simply be to:  cube both numerator and denominator.  Therefore when you take the cube root of each you will have this answer.

For example:  `(root(3)(x^3))/(root(3)(y^3)) = x/y`

Therefore:  3a^2 all cubed would be equivalent to:

`(3a^2)^3= 3^3*a^6=27a^6`

Next:  4b^3 all cubed would be equivalent...

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One way to do this would simply be to:  cube both numerator and denominator.  Therefore when you take the cube root of each you will have this answer.

For example:  `(root(3)(x^3))/(root(3)(y^3)) = x/y`

Therefore:  3a^2 all cubed would be equivalent to:

`(3a^2)^3= 3^3*a^6=27a^6`

Next:  4b^3 all cubed would be equivalent to:

`(4b^3)^3=4^3*b^9=64b^9`

Now just write each expression as the cube root in the numerator and denominator respectively as:

 

`root(3)(27a^6)/root(3)(64b^9)`

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