\sqrt[3]{16 {x}^(4) } - \sqrt[3]{128x} Simplify terms to identify the like radicals. Assume that all variables represent positive real numbers.

Question

`\sqrt[3]{16 {x}^(4) } - \sqrt[3]{128x}`

Simplify terms to identify the like radicals. Assume that all variables represent positive real numbers.

Answer 1

Kudos to the poster on the typeset math.

With cube roots we don't have to worry that things are positive.

`\sqrt[3]{16 x^4} - \sqrt[3]{128 x} = \sqrt[3]{2^4 x^4} - \sqrt[3]{2^7 x} = \sqrt[3]{2^3 x^3 2x} - \sqrt[3]{4^3 2 x} = 2x\sqrt[3]{2x} - 4\sqrt[3]{2 x}`

`= (2x-4)\sqrt[3]{2 x}`