1. **State the problem:** Simplify the expression $$\left(\frac{125}{64}\right)^{\frac{2}{3}}$$ and find which of the given options matches the result. 2. **Recall the exponent rule:** For any positive numbers $a$ and $b$, and rational exponent $m/n$, we have $$\left(\frac{a}{b}\right)^{\frac{m}{n}} = \frac{a^{\frac{m}{n}}}{b^{\frac{m}{n}}}$$ 3. **Apply the rule:** $$\left(\frac{125}{64}\right)^{\frac{2}{3}} = \frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$$ 4. **Evaluate the cube roots:** $$125^{\frac{1}{3}} = 5 \quad \text{since } 5^3 = 125$$ $$64^{\frac{1}{3}} = 4 \quad \text{since } 4^3 = 64$$ 5. **Raise to the power 2:** $$125^{\frac{2}{3}} = \left(125^{\frac{1}{3}}\right)^2 = 5^2 = 25$$ $$64^{\frac{2}{3}} = \left(64^{\frac{1}{3}}\right)^2 = 4^2 = 16$$ 6. **Combine the results:** $$\frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}} = \frac{25}{16}$$ 7. **Final answer:** The expression simplifies to $$\boxed{\frac{25}{16}}$$ which corresponds to option B.