SOLUTION: 3^3√64x+3^3√27x simplify and combine

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Question 169922: 3^3√64x+3^3√27x
simplify and combine
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Aroot%283%2C64x%29%2B3%2Aroot%283%2C27x%29 Start with the given expression


3%2Aroot%283%2C4%5E3x%29%2B3%2Aroot%283%2C3%5E3x%29 Rewrite 64 as 4%5E3. Rewrite 27 as 3%5E3


3%2Aroot%283%2C4%5E3%29%2Aroot%283%2Cx%29%2B3%2Aroot%283%2C3%5E3%29%2Aroot%283%2Cx%29 Break up the roots. Note: root%283%2C4%5E3x%29=root%283%2C4%5E3%29%2Aroot%283%2Cx%29


3%2A4%2Aroot%283%2Cx%29%2B3%2A3%2Aroot%283%2Cx%29 Take the cube root of 4%5E3 to get 4. Take the cube root of 3%5E3 to get 3


12%2Aroot%283%2Cx%29%2B9%2Aroot%283%2Cx%29 Multiply


Let z=root%283%2Cx%29


12z%2B9z Replace root%283%2Cx%29 with "z"


21z Combine like terms.


21%2Aroot%283%2Cx%29 Plug in z=root%283%2Cx%29


So 3%2Aroot%283%2C64x%29%2B3%2Aroot%283%2C27x%29=21%2Aroot%283%2Cx%29