Solve the following equation with a rational exponent: x 2/3=64 .(1 point)

To solve the equation \( x^{2/3} = 64 \), we can raise both sides to the power of \(\frac{3}{2}\) to isolate \(x\).

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

This simplifies to:

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

Next, we calculate \(64^{3/2}\).

1. Find \(64^{1/2}\):
\[
64^{1/2} = 8
\]

2. Then, raise that result to the power of 3:
\[
8^3 = 512
\]

So, \(64^{3/2} = 512\).

Now we have:

\[
x = 512
\]

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

\[
\boxed{512}
\]