SOLUTION: I should write this problem in exponential for and simplify.... I know how that works (usually) I just dont get how to do it with this problem; cubed root of "a" times the fith ro

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I should write this problem in exponential for and simplify.... I know how that works (usually) I just dont get how to do it with this problem; cubed root of "a" times the fith ro      Log On


   

Question 214160: I should write this problem in exponential for and simplify.... I know how that works (usually) I just dont get how to do it with this problem;
cubed root of "a" times the fith root of "a".....
3_________________________5
v---- < (the v--- is the sqrt.) times v--- (just ignore the _____)
__a_________________________a
Hope my "doodling" helped a bit.....
Found 3 solutions by Alan3354, jim_thompson5910, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
should write this problem in exponential for and simplify.... I know how that works (usually) I just dont get how to do it with this problem;
cubed root of "a" times the fith root of "a".....
--------------
= a%5E%281%2F3%29%2Aa%5E%281%2F5%29
Add exponents when multiplying.
= a%5E%281%2F3+%2B+1%2F5%29
= a%5E%288%2F15%29
The exponent is 8/15, in case it's obscured.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2Ca%29%2Aroot%285%2Ca%29 Start with the given expression


%28a%5E%281%2F3%29%29%2A%28a%5E%281%2F5%29%29%5E%22%22 Convert to exponential notation.


a%5E%281%2F3%2B1%2F5%29%5E%22%22 Use the identity x%5Ey%2Ax%5Ez=x%5E%28y%2Bz%29 to multiply


a%5E%288%2F15%29%5E%22%22 Add the fractions.


root%2815%2Ca%5E8%29 Convert back to radical notation.


So root%283%2Ca%29%2Aroot%285%2Ca%29=root%2815%2Ca%5E8%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I think you are trying to render:



The trick here is to recognize that



So you have:



Next use:



Then since:



We have:




John