Simplify. Assume all variable are positive

Question

1.) 6∛2-∛16 (third root)

2.) √x⁸y⁹

^3.) ∜x⁸/y^{4 (foruth root)}

^{4.) 11}√x+5√x

Answer 1

1) Since 16 is the same as 2•8 and the cube root of 8 is 2, then the cube root of 16 = 2cuberoot(2). Then 6cuberoot(2) - 2cuberoot(2) = 4cuberoot(2)

2) √x⁸ = x⁴ and √y⁹ = √(y•y⁸) = y⁴√y

So √(x⁸y⁹) = x⁴y⁴√y

3) fourthroot(x⁸) = x² and fourthroot(y⁴) = y

So fourthroot(x⁸/y⁴) = x²/y

4) I think you mean 11√x + 5√x (as opposed the the eleventh root of x). If so, just think of √x as "apples". 11 apples plus 5 apples is 16 apples. So 11√x + 5√x = 16√x