Question

What is the simplified form of the following expression?

Answer 1

C

Explanation:

Answer 2

For this case we must simplify the following expression:
`7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})`

We rewrite:

`16x = 2 ^ 3 * 2x\\8x = 2 ^ 3 * x`

We rewrite the expression:

`7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {2 ^ 3 * 2x}) - 3 (\sqrt [3] {2 ^ 3 * x}) =`

By definition of properties of powers and roots we have:

`\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}`

Then, taking the terms of the radical:

`7 (\sqrt [3] {2x}) - 3 (2 \sqrt [3] {2x}) - 3 (2 \sqrt [3] {x}) =\\7 \sqrt [3] {2x} -6 \sqrt [3] {2x} -6 \sqrt [3] {x} =`

We add similar terms:

`\sqrt [3] {2x} -6 \sqrt [3] {x}`

Answer:

Option C