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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:
\[
\boxed{512}
\]