1. **State the problem:** Simplify the expression $64^{\frac{2}{3}}$. 2. **Recall the rule for fractional exponents:** For any positive number $a$ and rational exponent $\frac{m}{n}$, we have $$a^{\frac{m}{n}} = \left(\sqrt[n]{a}\right)^m = \sqrt[n]{a^m}$$ This means we can either take the $n$th root first and then raise to the $m$th power, or vice versa. 3. **Apply the rule to $64^{\frac{2}{3}}$:** Here, $a=64$, $m=2$, and $n=3$. 4. **Find the cube root of 64:** $$\sqrt[3]{64} = 4$$ because $4^3 = 64$. 5. **Raise the result to the power 2:** $$4^2 = 16$$ 6. **Therefore,** $$64^{\frac{2}{3}} = 16$$ **Final answer:** $16$