Question

What is the simplified form of the following expression?

Answer 1

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