Multiply Radicals and Simplify

[justan4cat]

Could you please point me in the right direction? I’ve asked for help in the classroom, but I’m not getting any responses. I have until 3am to submit this. It’s going to be a late night. I don't understand how to type it here, but I'll try. I can't find the rules for multiplying when the index is different. Any help would be appreciated!

Multiply and Simplify:

the square root of x^2y^3 * the cube root of xy^4

 

[BigGlenntheHeavy]

\(\displaystyle (x^2y^3)^{1/2}(xy^4)^{1/3} \ = \ (xy^{3/2})(x^{1/3}y^{4/3})\)

\(\displaystyle = \ x^{4/3}y^{17/6} \ = \ xy^2(x^{1/3}y^{5/6})\)

 

[justan4cat]

and one last step, and I got it... oh, thank you so very much!

xy[sup:3isw57iv]2[/sup:3isw57iv] (x[sup:3isw57iv]2/6[/sup:3isw57iv]y[sup:3isw57iv]5/6[/sup:3isw57iv]) = xy[sup:3isw57iv]2[/sup:3isw57iv] 6th root of x[sup:3isw57iv]2[/sup:3isw57iv]y[sup:3isw57iv]5[/sup:3isw57iv]