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

To solve the equation \( x^{2/3} = 64 \), we need to isolate \( x \).

First, we can eliminate the rational exponent by raising both sides of the equation to the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):

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

The left side simplifies to:

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

Now we calculate the right side:

\[
64^{3/2} = (64^{1/2})^3
\]

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

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

Now raise that result to the power of 3:

\[
8^3 = 512
\]

Thus, we have:

\[
x = 512
\]

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

\[
\boxed{512}
\]