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

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

1. **Isolate \( x \)**: To eliminate the rational exponent, raise both sides of the equation to the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\):

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

2. **Simplify the left side**:

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

3. **Calculate the right side**:

First, calculate \( 64^{1/2} \) (the square root of 64):

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

Now, raise that to the power of 3:

\[
8^3 = 512
\]

4. **Thus, we have**:

\[
x = 512
\]

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

\(\boxed{512}\).