SOLUTION: I am trying to figure this problem out and I need some help with it. I am working with cube roots and I am stuck on this problem: ∛(54x^10 y^2 z^15 ) I know that 54 can b

Algebra ->  Square-cubic-other-roots -> SOLUTION: I am trying to figure this problem out and I need some help with it. I am working with cube roots and I am stuck on this problem: ∛(54x^10 y^2 z^15 ) I know that 54 can b      Log On


   

Question 995381: I am trying to figure this problem out and I need some help with it. I am working with cube roots and I am stuck on this problem:
∛(54x^10 y^2 z^15 )
I know that 54 can be cubed so I get 3^3*2. But I can't figure out how to finish this problem. Can you help me?
Found 3 solutions by josgarithmetic, macston, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2C54x%5E10y%5E2z%5E15%29
root%283%2C2%2A3%5E3%2Ax%5E10y%5E2%2Az%5E15%29


3%2Ax%2Ax%2Ax%2Az%2Az%2Az%2Az%2Az%2Aroot%283%2C2%2Ay%5E2%29
highlight%283x%5E3z%5E5%2Aroot%283%2C2y%5E2%29%29

Any three occurrences of a factor k inside this radical becomes a single factor outside
of this radical. root%283%2Ck%5E3%29=k.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
root%283%2C%2854x%5E10y%5E2z%5E15%29%29=
.
=
.
=
.
%283x%5E3z%5E5%29%28root%283%2C2xy%5E2%29%29
.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

I am trying to figure this problem out and I need some help with it. I am working with cube roots and I am stuck on this problem:
∛(54x^10 y^2 z^15 )
I know that 54 can be cubed so I get 3^3*2. But I can't figure out how to finish this problem. Can you help me?
root+%283%2C+54x%5E10y%5E2z%5E15%29

root+%283%2C+27+%2A+2+%2A+x%5E9+%2A+x+%2A+y%5E2+%2A+z%5E15%29

root+%283%2C+3%5E3+%2A+2+%2A+%28x%5E3%29%5E3+%2A+x+%2A+y%5E2+%2A+%28z%5E5%29%5E3%29

highlight_green%283x%5E3z%5E5+%2A+root+%283%2C+2xy%5E2%29%29%29