Question

Please correct my work and show your work if I MESSED up

Answer 1

If the first line says

$\sqrt[3]{4x^3}\cdot\sqrt[3]{2x^4}$

we should first write this as one cube root:

$\sqrt[3]{4x^3\cdot2x^4}=\sqrt[3]{8x^7}$

Then for any factor under the cube root, we extract any 3rd powers we can. Since $8=2^3$ and $x^7=x^6\cdot x=(x^2)^3\cdot x$, we have

$\sqrt[3]{8x^7}=\sqrt[3]{2^3(x^2)^3x}=\sqrt[3]{(2x^2)^3x}=\sqrt[3]{(2x^2)^3}\cdot\sqrt[3]x=2x^2\cdot\sqrt[3]x$

Then [1] = $2x^2$ and [2] = $x$.