SOLUTION: Simplify: the cubed root of 64 divided by the cubed root of x squared. What I've done: simplified the cubed root of 64 to 4. Then multiplied the the cubed root of x to the 4 powe

Algebra ->  Radicals -> SOLUTION: Simplify: the cubed root of 64 divided by the cubed root of x squared. What I've done: simplified the cubed root of 64 to 4. Then multiplied the the cubed root of x to the 4 powe      Log On


   



Question 687912: Simplify: the cubed root of 64 divided by the cubed root of x squared.
What I've done: simplified the cubed root of 64 to 4. Then multiplied the the cubed root of x to the 4 power times 4 over the cubed root of x squared. I then got 4 times the cubed root of x to the forth power over the cubed root of x to the eighth power. I then simplified it to 4 times the cubed root of x to the fourth power over x squared, but that is not the correct answer according to my answer sheet. Can you tell me where I went wrong and/or how to fix it so I get the answer of 4 times the cubed root of x over x?

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify: the cubed root of 64 divided by the cubed root of x squared.
What I've done: simplified the cubed root of 64 to 4. Then multiplied the the cubed root of x to the 4 power times 4 over the cubed root of x squared. I then got 4 times the cubed root of x to the forth power over the cubed root of x to the eighth power. I then simplified it to 4 times the cubed root of x to the fourth power over x squared, but that is not the correct answer according to my answer sheet. Can you tell me where I went wrong and/or how to fix it so I get the answer of 4 times the cubed root of x over x?

root%283%2C+64%29%2Froot%283%2C+x%5E2%29

root%283%2C+64%29%2Froot%283%2C+x%5E2%29 * root%283%2C+x%29%2Froot%283%2C+x%29 ----- Rationalize the denominator by multiplying by 1, which is the same as multiplying both by root%283%2C+x%29

root%283%2C+64x%29%2Froot%283%2C+x%5E3%29 ------- root%283%2C+4%5E3x%29%2Froot%283%2C+x%5E3%29 ---- highlight_green%284root%283%2C+x%29%2Fx%29

You can do the check!!

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