Solve the following equation with a rational exponent: 2x32=16.(1 point) Responses 8 8 4 4 84 84 no solution

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:
\[
\boxed{4}
\]