SOLUTION: please show the work on how to get the third root of 9 divided by the fifth root of 27. I know the answer is fifteenth root of 3, but how do you get that answer?

Algebra ->  Square-cubic-other-roots -> SOLUTION: please show the work on how to get the third root of 9 divided by the fifth root of 27. I know the answer is fifteenth root of 3, but how do you get that answer?      Log On


   



Question 418967: please show the work on how to get
the third root of 9 divided by the fifth root of 27. I know the answer is fifteenth root of 3, but how do you get that answer?

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how to get
the third root of 9 divided by the fifth root of 27. I know the answer is fifteenth root of 3
---
9^(1/3) = 3^(2/3)
-----------
27^(1/5) = 3^(3/5)
========================
[3^(2/3)]/[3^(3/5)]
---
= 3^[2/3 - 3/5]
---
= 3^[(10-9)/15]
---
= 3^(1/15)
================
Cheers,
Stan H.
===================