1. **Stating the problem:** Simplify the expression $$\left(\frac{2b}{5c}\right)^2$$. 2. **Formula used:** When raising a fraction to a power, apply the exponent to both numerator and denominator: $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$ 3. **Apply the formula:** $$\left(\frac{2b}{5c}\right)^2 = \frac{(2b)^2}{(5c)^2}$$ 4. **Simplify numerator and denominator:** $$\frac{(2)^2 (b)^2}{(5)^2 (c)^2} = \frac{4b^2}{25c^2}$$ 5. **Final answer:** $$\boxed{\frac{4b^2}{25c^2}}$$