1. **State the problem:** Evaluate $$\left[ \left(-\frac{4}{11}\right)^{\frac{4}{5}} \cdot \left(-\frac{4}{11}\right)^{-\frac{4}{5}} \right]^7$$. 2. **Recall the exponent rule:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$. 3. **Apply the rule inside the bracket:** $$\left(-\frac{4}{11}\right)^{\frac{4}{5}} \cdot \left(-\frac{4}{11}\right)^{-\frac{4}{5}} = \left(-\frac{4}{11}\right)^{\frac{4}{5} + (-\frac{4}{5})} = \left(-\frac{4}{11}\right)^0$$. 4. **Simplify the exponent:** Any nonzero number raised to the zero power is 1: $$\left(-\frac{4}{11}\right)^0 = 1$$. 5. **Raise the result to the 7th power:** $$1^7 = 1$$. **Final answer:** $$1$$.