Answer:
[tex]7xy^{2} \sqrt[3]{2xy}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{686x^{4} y^{7}}[/tex]
[tex]686 = 343 * 2[/tex]
[tex]x^{4} = x^{3} * x[/tex]
[tex]y^{7} = y^{3} * y^{3} * y[/tex]
[tex]\sqrt[3]{343} =7[/tex]
[tex]\sqrt[3]{x^{3}} = x[/tex]
[tex]\sqrt[3]{y^{3}* y^{3}}[/tex] = [tex]y^{2}[/tex]
so you're left with 2, x, and y inside the cube root, and 7, x, and y^2 outside
[tex]7xy^{2} \sqrt[3]{2xy}[/tex]
