SOLUTION: can you explain how to simplify {{{root(3,ab^2)root(3,a^2b^5)}}}

Break everything down to prime factors with no exponents other than 1:



Put everything under just one cube root radical:



Now, since the index of the cube root is 3, make as many groups of 
three like factors as possible.



Each of those groups of three like factors represents a cube, and 
will come outside the radical as just a single factor.

The  is just  and comes out of the radical as a 
single 



The  is just  and comes out of the radical as a 
single 



The other  likewise comes out of the radical as a single 



The only thing left under the radical is the  which was left
over after all possible groups of three like factors were made. So
the final answer is



Edwin