Which expression is equivalent to 3 square root 256x^10y^7?

The correct answer is
$4x^3y^2(\sqrt[3]{4xy})$ .

When we list the prime factorization of 256x^10y^7, we want to look for triples (this is a cubed root):

256 = 2³(2³)(2²)
x^10 = x³(x³)(x³)x
y^7 = y³(y³)y

Taking out our triples, we have
2*2*x*x*x*y*y outside the cubed root, with 2²(x)(y) left inside:

$2(2)(x)(x)(x)(y)(y)\sqrt[3]{2^2xy} \\ \\=4x^3y^2\sqrt[3]{4xy}$