Simplify. Assume all variables represent positive real numbers

Question

Simplify assume all the variables are positive real numbers 

 

³√x^6y^5

Answer 1

If you remember,  ^a√x = x^1/a

and x^(a•b) = (x^a)^b

 

we can take your eqn ³√x⁶y⁵

 

and convert it to

 

 ³√x⁶y⁵ = (x⁶y⁵)^1/3= x^6/3 y^5/3 

 

x^6/3  simplifies to x² because 6/3 = 2

y^5/3  simplifies to y(³√y²⁾  because y^5/3 = y^(3+2)/3 = y^3/3 y^2/3 = y(³√y²)  which doesn't look very simplified,but it is

 

so your answer would be

 

x²y (³√y2)