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

To solve the equation \( X^{\frac{2}{3}} = 64 \), we can start by raising both sides of the equation to the reciprocal of the exponent, which is \( \frac{3}{2} \).

\[
X = 64^{\frac{3}{2}}
\]

Now we can simplify \( 64^{\frac{3}{2}} \):

1. First, find the square root of 64:
\[
\sqrt{64} = 8
\]

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

Thus, we have:
\[
X = 512
\]

So the solution to the equation \( X^{\frac{2}{3}} = 64 \) is:

\(\boxed{512}\)