SOLUTION: ∛((729x^14)/y^3 ) Simplify by taking roots of the numberator and denominator Could someone please help me with this one.

Algebra ->  Radicals -> SOLUTION: ∛((729x^14)/y^3 ) Simplify by taking roots of the numberator and denominator Could someone please help me with this one.      Log On


   

Question 285834: ∛((729x^14)/y^3 )
Simplify by taking roots of the numberator and denominator

Could someone please help me with this one.
Found 2 solutions by stanbon, Grinnell:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
∛((729x^14)/y^3 )
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= (9^3x^12/y^3)^1/3 * cbrt(x^2)
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= (9x^4/y)*cbrt(x^2
OR
= (9x^4/y)*x^(2/3)
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Cheers,
Stan H.

Answer by Grinnell(63) About Me  (Show Source):
You can put this solution on YOUR website!
Breath in, breath out, we WILL get thru this! LOL
If I understand this correctly we have the cubed root of the entire quantity 729x^14/y^3, correct?
Look what we have, some perfect cubes!!!
let's pull the 9 out of the numerator and from underneath the radical, let's do the same for the y in the denominatorso we get 9/y TIMES cubed root of x^14. (YOU MUST KNOW THE LAWS OF EXPONENTS--GO BACK AND REVIEW!!!) x^14(1/3) is the same as cubed root of x^14. x^14/3 =x^4 with 2/3 left, soo
we also pull an x^4 out. NOW we have a 9x^4/yTIMES x^2/3=9x^4/y TIMES cubed root of x^2
9x^4/y TIMES cubed root of x^2, this is the answer! is this clear? let me hear from you Be sure to put 'cube problem' in your response.