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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
\(\boxed{512}\).