Simplify the radical expression

Question

Simplify the radical expression. All variables represent positive real numbers.

 

fourth-root 162(x^12)(y^4)

Answer 1

The 4th root of a number is the same as raising the number to the 1/4 power.

 

So, we have (162x¹²y⁴)^¼ = (162)^¼(x¹²)^¼(y⁴)^¼

 

                                             = (81)^¼(2)^¼x³y

 

                                              = 3 (⁴√2) x³y