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`.