Question 278977
How do you figure out the cube root of x times the fifth root of y?
<pre><font size = 4 color = "indigo"><b>
{{{root(3,x)*root(5,y)}}}

Change the roots to fraction exponents:

{{{drawing(800,70,-1,38,-2,2,locate(0,1,

root(3,x)*root(5,y)=x^(1/3)y^(1/5)   ))}}} 

Get the fraction exponents with their least common denominator:

{{{drawing(800,70,-1,38,-2,2,locate(0,1,
root(3,x)*root(5,y)=x^(1/3)y^(1/5)=x^(5/15)y^(3/15)   ))}}}

Change each to a 15th root:

{{{drawing(800,70,-1,38,-2,2,locate(0,1,
root(3,x)*root(5,y)=x^(1/3)y^(1/5)=x^(5/15)y^(3/15)=root(15,x^5)*root(15,y^3)   ))}}}

Now since the radicals have the same index, you can multiply
under them:

{{{drawing(800,70,-1,38,-2,2,locate(0,1,
root(3,x)*root(5,y)=x^(1/3)y^(1/5)=x^(5/15)y^(3/15)=root(15,x^5)*root(15,y^3)=root(15,x^5y^3)   ))}}} 

Edwin</pre>