To solve the equation \( x^{\frac{2}{3}} = 64 \), we can first isolate \( x \) by raising both sides of the equation to the reciprocal of the exponent \( \frac{2}{3} \), which is \( \frac{3}{2} \).
\[ x = 64^{\frac{3}{2}} \]
Now we can calculate \( 64^{\frac{3}{2}} \).
First, find the square root of \( 64 \):
\[ \sqrt{64} = 8 \]
Next, raise that result to the power of 3:
\[ 8^3 = 512 \]
Therefore, the solution to the equation \( x^{\frac{2}{3}} = 64 \) is:
\[ x = 512 \]
Thus, among the response options, the answer is 512.