SOLUTION: Hello, I have a question on simplifying radicals such as this one {{{(81)^(1/3)}}}. the answer to it is {{{3(3^(1/3))}}} but I would like to know how you reach that answer. Tha

Algebra ->  Radicals -> SOLUTION: Hello, I have a question on simplifying radicals such as this one {{{(81)^(1/3)}}}. the answer to it is {{{3(3^(1/3))}}} but I would like to know how you reach that answer. Tha      Log On


   

Question 986891: Hello,
I have a question on simplifying radicals such as this one %2881%29%5E%281%2F3%29.
the answer to it is 3%283%5E%281%2F3%29%29 but I would like to know how you reach that answer.
Thanks in advance!!
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
3(3^(1/3)

According with rules of handling exponents,
3*3^(1/3)=3^(1+1/3)=3^(4/3)

Rendering might not show too well but ....
3%2A3%5E%281%2F3%29=3%5E%281%2B1%2F3%29=3%5E%284%2F3%29

---
Trying to simplify original expression:
81%5E%281%2F3%29
%289%5E2%29%5E%281%2F3%29
%283%5E4%29%5E%281%2F3%29
3%5E%284%2A%281%2F3%29%29
and your expected answer does not seem to be the only or best, but...
3%5E%284%2F3%29-----which what I would stay with,...
3%5E%284%2F3%29=3%5E%283%2F3%2B1%2F3%29
3%5E%281%2B1%2F3%29
3%2A3%5E%281%2F3%29-------but why?