The problem you have written
[tex]\sqrt[5]{x^{10}}/2[/tex]
simplifies to
[tex]x^2/2=\dfrac{x^2}{2}[/tex]
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If you intend
[tex]\sqrt[5]{x^{10}/2}[/tex]
then you can multiply by the appropriate fraction to get your first answer choice.
[tex]\displaystyle\sqrt[5]{\frac{x^{10}}{2}}=\frac{\sqrt[5]{x^{10}}}{\sqrt[5]{2}}\cdot\frac{\sqrt[5]{2^4}}{\sqrt[5]{2^4}}\\\\=\frac{x^{2}\sqrt[5]{16}}{\sqrt[5]{2^{5}}}=\bf{\frac{x^{2}\sqrt[5]{16}}{2}}[/tex]
