1. **State the problem:** Simplify the expression $$\frac{\left(\frac{2}{7}\right)^{-2}}{\left(\frac{7}{2}\right)^2}$$. 2. **Recall the rules:** - Negative exponent rule: $$a^{-n} = \frac{1}{a^n}$$. - Power of a fraction: $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$. - Division of fractions: $$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \times \frac{d}{c}$$. 3. **Apply the negative exponent:** $$\left(\frac{2}{7}\right)^{-2} = \left(\frac{7}{2}\right)^2$$. 4. **Rewrite the expression:** $$\frac{\left(\frac{7}{2}\right)^2}{\left(\frac{7}{2}\right)^2}$$. 5. **Since numerator and denominator are the same:** $$= 1$$. **Final answer:** $$1$$.