SOLUTION: Ughhhh... This algebra is so hard. I would really appreciate any help someone could give me. Thank you so much in advance!!!!!! Simplify by factoring, assume that all numbers un

Algebra ->  Radicals -> SOLUTION: Ughhhh... This algebra is so hard. I would really appreciate any help someone could give me. Thank you so much in advance!!!!!! Simplify by factoring, assume that all numbers un      Log On


   

Question 242356: Ughhhh... This algebra is so hard. I would really appreciate any help someone could give me. Thank you so much in advance!!!!!!
Simplify by factoring, assume that all numbers under the radical are nonnegative.
3rd root of 270*t^8
That would be 270*t^8 under the radical sign, and the 3, up in the checkmark on the outside of the radical sign.
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use these exponentiation rules
%28x%5EM%29%2A%28x%5EN%29=x%5E%28M%2BN%29+
%28x%5E%28M%29%29%5EN=x%5E%28M%2AN%29
.
.
.
+%28270%2At%5E8%29%5E%281%2F3%29=%2827%2A10%2At%5E6%2At%5E2%29%5E%281%2F3%29

27=3%5E3
27%5E%281%2F3%29=%283%5E3%29%5E%281%2F3%29=3
%28t%5E6%29%5E%281%2F3%29=t%5E2
%28270%2At%5E8%29%5E%281%2F3%29=3t%5E2%2A%2810t%5E2%29%5E%281%2F3%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
3rd root of 270*t^8
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Factor 270t^8 into a perfect cube and another factor
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270t^8 = (27t^6)*(10t^2)
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Take the 3rd root of each of those factors to get the answer:
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= (3t^2)*3rd rt of (10t^2)
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That is as much simplifying as you can do.
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Cheers,
Stan H.