Express $\left(64^{\frac{1}{3}}\right)^{2}$ in simplest radical form.

Step 1 ：The given expression is \(\left(64^{\frac{1}{3}}\right)^{2}\).

Step 2 ：We know that \(64^{\frac{1}{3}}\) is the cube root of 64.

Step 3 ：The cube root of 64 is 4 because \(4^3 = 64\).

Step 4 ：So, we can replace \(64^{\frac{1}{3}}\) with 4.

Step 5 ：Then, we have to square 4 to get the final answer.

Step 6 ：The simplest radical form of \(\left(64^{\frac{1}{3}}\right)^{2}\) is \(\boxed{16}\).