^3√16x^3y^7 ("Cube root of 16x cubed times y to the seventh power")

Question

I'm confused with how to correctly simplify this expression because I got 2xy^2^3√2y ("2xy squared times the cube root of 2y) but when I tried to check my answer using a simplifying radical expressions calculator online, it gave me 2 ^3√2 xy^7/3 ("2 times the cube root of 2 times xy to the 7/3 power"). I was mostly thrown off by the "7/3 power" because when I simplified the " y to the 7th" component that was under the cube root, I thought it simplifies to "y squared times cube root of y" because there are two cubes within "y to the seventh." I'm really confused and I'm sorry that reading this might be confusing as well because of all the symbols, but I would really appreciate help!

Answer 1

³√(16x³y⁷)

16^1/3(x³)^1/3(y⁷)^1/3

(2³)^1/3(2^1/3)(x)(y⁶)^1/3(y)^1/3

2(2^1/3)(x)(y²)(y^1/3)

(2xy²)( ³√2y)