Answer:
C. [tex]x^3\cdot \sqrt[3]{x}[/tex]
Step-by-step explanation:
You are given the expression [tex]\sqrt[3]{x^{10}}[/tex]
Rewrite [tex]x^{10}[/tex] as [tex]x^3\cdot x^3\cdot x^3\cdot x[/tex]
Now
[tex]\sqrt[3]{x^{10}}=\sqrt[3]{x^3\cdot x^3\cdot x^3\cdot x}[/tex]
For odd n, use the property of radicals
[tex]\sqrt[n]{ab} =\sqrt[n]{a} \cdot\sqrt[n]{b}[/tex]
Hence
[tex]\sqrt[3]{x^{10}}=\sqrt[3]{x^3\cdot x^3\cdot x^3\cdot x}=\sqrt[3]{x^3}\cdot \sqrt[3]{x^3}\cdot \sqrt[3]{x^3}\cdot \sqrt[3]{x}=x\cdot x\cdot x\cdot\sqrt[3]{x}=x^3\cdot \sqrt[3]{x}[/tex]
