To simplify the expression \( x^{16} \cdot x^{16} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
Applying this property:
\[ x^{16} \cdot x^{16} = x^{16 + 16} = x^{32} \]
Now, none of the given responses directly match \( x^{32} \). Instead, we should try to determine if any of the choices can somehow be manipulated or simplified to equal \( x^{32} \).
As none of the options clearly align with \( x^{32} \), I'll analyze each option to check if they can be transformed into \( x^{32} \):
- \( 1/x\sqrt[3]{\sqrt{x}} \)
- \( x^{-\sqrt{x}} \)
- \( x^{-3\sqrt[3]{x}} \)
- \( 36 \)
None of these options seem to bring us to \( x^{32} \).
As a conclusion, the final answer \( x^{32} \) from the initial expression \( x^{16} \cdot x^{16} \) does not seem to align with any of the provided options based on common interpretations.
If this is a test question and the options are indeed presented as they are, then it’s possible that either there was a mistake in the response choices or they correspond to more complex interpretations. Based purely on the simplification of the expression using exponent properties, the correct answer would be \( x^{32} \).