For this case we must simplify the following expression:[tex]7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})[/tex]
We rewrite:
[tex]16x = 2 ^ 3 * 2x\\8x = 2 ^ 3 * x[/tex]
We rewrite the expression:
[tex]7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {2 ^ 3 * 2x}) - 3 (\sqrt [3] {2 ^ 3 * x}) =[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
Then, taking the terms of the radical:
[tex]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} =[/tex]
We add similar terms:
[tex]\sqrt [3] {2x} -6 \sqrt [3] {x}[/tex]
Answer:
Option C
