Question 199283
Use rational exponents to write x^1/5*y^1/3*z^1/6 as a single radical expression. 
<pre><font size = 4 color = "indigo"><b>
{{{drawing(100,60,0,5,-5,2, locate(0,0,x^(1/5)*y^(1/3)*z^(1/6)) )}}}

Get the common denominator of all those denominators
of the exponents

That is we want the LCM of 5,3,6, which is 30

So we write {{{1/5}}} as {{{6/30}}}
we write {{{1/3}}} as {{{10/30}}}
and we write {{{1/6}}} as {{{5/30}}}

{{{drawing(150,60,0,5,-5,2, locate(0,0,x^(6/30)*y^(10/30)*z^(5/30)) )}}}

Now use the principle {{{drawing(100,60,0,5,-5,2, 
locate(0,0,A^(M/N)=root(N,A^M))  )}}}
on each factor:

{{{root(30,x^6)root(30,y^10)root(30,z^5)}}}

and then multiply under the radicals with common
index:

{{{root(30,x^6y^10z^5)}}}

That's a single radical expresion.

Edwin</pre>