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