To simplify the expression \( x^{16} \cdot x^{16} \) using the properties of exponents, we can apply the property that states when multiplying two expressions with the same base, we add the exponents.
So, we have:
\[ x^{16} \cdot x^{16} = x^{16 + 16} = x^{32} \]
Therefore, the expression equivalent to \( x^{16} \cdot x^{16} \) is \( x^{32} \).