Answer:
The third option listed: [tex]\sqrt[3]{2x} -6\sqrt[3]{x}\\[/tex]
Step-by-step explanation:
We start by writing all the numerical factors inside the qubic roots in factor form (and if possible with exponent 3 so as to easily identify what can be extracted from the root):
[tex]7\sqrt[3]{2x} -3\sqrt[3]{16x} -3\sqrt[3]{8x} =\\=7\sqrt[3]{2x} -3\sqrt[3]{2^32x} -3\sqrt[3]{2^3x} =\\=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]
And now we combine all like terms (notice that the only two terms we can combine are the first two, which contain the exact same radical form:
[tex]7\sqrt[3]{2x} -6\sqrt[3]{2x} -6\sqrt[3]{x}=\\=\sqrt[3]{2x} -6\sqrt[3]{x}[/tex]
Therefore this is the simplified radical expression: [tex]\sqrt[3]{2x} -6\sqrt[3]{x}\\[/tex]
