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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:
\[
\boxed{512}
\]