Discussion

Explanation:

Given $\sqrt[ab]{x^{c^2}}\times \sqrt[bc]{x^{a^2}}\times \sqrt[ca]{{x^b}^2}$& 

= $x^{\frac{c^2}{ab}}\times x^{\frac{a^2}{bc}}\times x^{\frac{b^2}{ca}}$

= $x^{\frac{c^3}{abc}}\times x^{\frac{a^3}{abc}}\times x^{\frac{b^3}{abc}}$

= $x^{\frac{a^3+b^3+c^3}{abc}}$

Since, a + b + c = 0, it means a³ + b³ + c³ = 3abc

∴ $\sqrt[ab]{x^c}\times \sqrt[bc]{x^a}\times \sqrt[ca]{x^b}$ = $x^{\frac{3abc}{abc}}$ = x³

Hence, option (a).

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