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To solve the equation \( 2x^{3/2} = 16 \), we can follow these steps:
1. **Isolate the term with \( x \):**
\[
x^{3/2} = \frac{16}{2} = 8
\]
2. **Eliminate the rational exponent:**
To remove the exponent of \( \frac{3}{2} \), raise both sides to the reciprocal, which is \( \frac{2}{3} \):
\[
x = 8^{\frac{2}{3}}
\]
3. **Calculate \( 8^{\frac{2}{3}} \):**
We can express 8 as \( 2^3 \):
\[
8^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} = 2^{3 \cdot \frac{2}{3}} = 2^2 = 4
\]
Thus, the solution to the equation \( 2x^{3/2} = 16 \) is:
\[
\boxed{4}
\]