SOLUTION: I am trying to help my daughter Ember in her algebra class. 3^(10/3) change to as a radical expression? Explain. Secondly, simplify the resulting expression if possible.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am trying to help my daughter Ember in her algebra class. 3^(10/3) change to as a radical expression? Explain. Secondly, simplify the resulting expression if possible.       Log On


   

Question 576389: I am trying to help my daughter Ember in her algebra class.
3^(10/3) change to as a radical expression? Explain. Secondly, simplify the resulting expression if possible.

Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3^(10/3) change to as a radical expression? Explain. Secondly, simplify the resulting expression if possible.
----------
3%5E%2810%2F3%29+=+root%283%2C3%5E10%29
= root%283%2C3%5E9%2A3%29+=+3%5E3%2Aroot%283%2C3%29+=+27%2Aroot%283%2C3%29
-----------
Or,
3%5E%2810%2F3%29+=+3%5E%289%2F3%29%2A3%5E%281%2F3%29+=+3%5E3%2A3%5E%281%2F3%29
= 27%2Aroot%283%2C3%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the identity x%5E%28m%2Fn%29%5E%22%22=root%28n%2Cx%5Em%29 to get 3%5E%2810%2F3%29%5E%22%22=root%283%2C3%5E10%29


Optionally, you can evaluate 3%5E10 to get 59049, which would mean that 3%5E%2810%2F3%29%5E%22%22=root%283%2C59049%29


You can then further simplify root%283%2C59049%29 to get 27%2Aroot%283%2C3%29