Solve the following equation with a rational exponent: 2x32=16 .(1 point)

To solve the equation \( 2x^{3/2} = 16 \), follow these steps:

1. **Isolate the term with the variable:**

Divide both sides by 2:
\[
x^{3/2} = \frac{16}{2}
\]
\[
x^{3/2} = 8
\]

2. **Remove the rational exponent:**

To get rid of the exponent \(\frac{3}{2}\), we can raise both sides of the equation to the reciprocal of \(\frac{3}{2}\), which is \(\frac{2}{3}\):
\[
(x^{3/2})^{\frac{2}{3}} = 8^{\frac{2}{3}}
\]

The left side simplifies:
\[
x^{(3/2) \cdot (2/3)} = x^{1} = x
\]

Now we need to calculate \(8^{\frac{2}{3}}\). This can be done as follows:
\[
8^{\frac{2}{3}} = (8^{\frac{1}{3}})^2
\]

Since \(8^{\frac{1}{3}} = 2\) (because \(2^3 = 8\)), we have:
\[
8^{\frac{2}{3}} = (2)^2 = 4
\]

3. **Final Result:**
\[
x = 4
\]

Thus, the solution is \(\boxed{4}\).