To simplify \( x^{1/6} \times x^{1/6} \), we use the properties of exponents. Specifically, when multiplying two expressions with the same base, we add their exponents:
\[ x^{1/6} \times x^{1/6} = x^{1/6 + 1/6} = x^{2/6} = x^{1/3} \]
Now we need to find an equivalent expression for \( x^{1/3} \) from the options given:
- \( 3^{\sqrt{x}} \)
- \( \sqrt{x} \)
- \( \frac{1}{\sqrt{x}} \)
- \( 36^{\sqrt{x}} \)
None of these options directly match \( x^{1/3} \). However, we can look for a way to express \( x^{1/3} \) in relation to these choices.
Since none of these options represents \( x^{1/3} \), we conclude that none of the provided expressions are equivalent to \( x^{1/6} \times x^{1/6} \).
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