SOLUTION: Can you help me simplify {{{(125^(2log(5,x)))(3^log(9,x)^10)}}}? Thanks!

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Question 275172: Can you help me simplify %28125%5E%282log%285%2Cx%29%29%29%283%5Elog%289%2Cx%29%5E10%29?
Thanks!
Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
Can you help me simplify %28125%5E%282log%285%2Cx%29%29%29%283%5Elog%289%2Cx%29%5E10%29?
Note that 125 = 5^3. We can rewrite the left-hand expression above as:
(5^3)^(2*log(5,x))=
5^(3*2*log(5,x)) =
5^(6*log(5,x)) =
5^(log(5,x^6) = x^6
Note that 3 = 9^(1/2). We can rewrite the right-hand expression above as:
(9^(1/3))^(log(9,x^10)) =
9^(1/3*log(9,x^10)) =
9^(log(9,(x^10)^1/3)) =
9^(log(9,x^10/3)) = x^10/3
Multiplying the two expressions then we have:
x^6 * x^10/3 = x^(6+(10/3)) = x^28/3