simplify the radical?

Question

cubic rt. (x^7y^11)

please show me work, i dont know how to get to the answer. thanx

Answer 1

x²y³∛(xy²)

Answer 2

cubic root (x^7y^11) = x^2y^3 cubic root (xy^2)

Answer 3

x^(7/3) y^(11/3)

Answer 4

first factor the exponential terms:
∛(x⁷y¹¹) = ∛(x³x³x¹y³y³y³y²)
Note that I broke it down into powers of 3.

now evaluate the radical factor-by-factor:
∛(x³x³xy³y³y³y²) = (∛x³) (∛x³) (∛x) (∛y³) (∛y³) (∛y³) (∛y²)
= (x)(x)(∛x)(y)(y)(y)(∛y²)
= x²y³∛(xy²)