If the first line says
[tex]\sqrt[3]{4x^3}\cdot\sqrt[3]{2x^4}[/tex]
we should first write this as one cube root:
[tex]\sqrt[3]{4x^3\cdot2x^4}=\sqrt[3]{8x^7}[/tex]
Then for any factor under the cube root, we extract any 3rd powers we can. Since [tex]8=2^3[/tex] and [tex]x^7=x^6\cdot x=(x^2)^3\cdot x[/tex], we have
[tex]\sqrt[3]{8x^7}=\sqrt[3]{2^3(x^2)^3x}=\sqrt[3]{(2x^2)^3x}=\sqrt[3]{(2x^2)^3}\cdot\sqrt[3]x=2x^2\cdot\sqrt[3]x[/tex]
Then [1] = [tex]2x^2[/tex] and [2] = [tex]x[/tex].
