Solve the following equation with a rational exponent: x2/3=64 .(1 point)

To solve the equation \( x^{2/3} = 64 \), follow these steps:

1. **Raise both sides to the reciprocal of the exponent**: The reciprocal of \( \frac{2}{3} \) is \( \frac{3}{2} \).

\[
(x^{2/3})^{\frac{3}{2}} = 64^{\frac{3}{2}}
\]

2. **Simplify the left side**:

\[
x^{(2/3) \cdot (3/2)} = x^1 = x
\]

3. **Calculate the right side**:

First, calculate \( 64^{1/2} \):

\[
64^{1/2} = \sqrt{64} = 8
\]

Now raise that result to the power of 3:

\[
64^{3/2} = 8^3 = 512
\]

4. **Write the final equation**:

\[
x = 512
\]

Thus, the solution to the equation \( x^{2/3} = 64 \) is

\[
\boxed{512}
\]