Question 149804
can you explain how to simplify 

{{{root(3,ab^2)root(3,a^2b^5)}}}
<pre><font size = 4 color = "indigo"><b>
Break everything down to prime factors with no exponents other than 1:

{{{root(3,abb)root(3,aabbbbb)}}}

Put everything under just one cube root radical:

{{{root(3,aaabbbbbbb)}}}

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

{{{root(3,(aaa)(bbb)(bbb)b)}}}

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

The {{{(aaa)}}} is just {{{a^3}}} and comes out of the radical as a 
single {{{a}}}

{{{a*root(3,(bbb)(bbb)b)}}}

The {{{(bbb)}}} is just {{{b^3}}} and comes out of the radical as a 
single {{{b}}}

{{{ab*root(3,(bbb)b)}}}

The other {{{(bbb)}}} likewise comes out of the radical as a single {{{b}}}

{{{abb*root(3,b)}}}

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

{{{ab^2*root(3,b)}}}

Edwin</pre>