1. **State the problem:** Simplify the expression $$\left(\left(-\frac{2}{9}\right)^8\right)^7$$. 2. **Use the power of a power rule:** When raising a power to another power, multiply the exponents: $$\left(a^m\right)^n = a^{m \times n}$$ 3. **Apply the rule:** $$\left(\left(-\frac{2}{9}\right)^8\right)^7 = \left(-\frac{2}{9}\right)^{8 \times 7} = \left(-\frac{2}{9}\right)^{56}$$ 4. **Evaluate the sign:** Since the base is negative and the exponent is even ($56$), the result is positive. 5. **Final simplified form:** $$\left(-\frac{2}{9}\right)^{56} = \frac{2^{56}}{9^{56}}$$ **Answer:** $$\frac{2^{56}}{9^{56}}$$