1. **State the problem:** Evaluate the expression $$\left[\left(-\frac{4}{11}\right)^{\frac{4}{5}} \cdot \left(-\frac{4}{11}\right)^{-\frac{4}{5}}\right].$$ 2. **Recall the exponent rule:** For any nonzero number $a$ and exponents $m$ and $n$, $$a^m \cdot a^n = a^{m+n}.$$ This means when multiplying powers with the same base, we add the exponents. 3. **Apply the rule:** Here, the base is $-\frac{4}{11}$, and the exponents are $\frac{4}{5}$ and $-\frac{4}{5}$. So, $$\left(-\frac{4}{11}\right)^{\frac{4}{5}} \cdot \left(-\frac{4}{11}\right)^{-\frac{4}{5}} = \left(-\frac{4}{11}\right)^{\frac{4}{5} + (-\frac{4}{5})} = \left(-\frac{4}{11}\right)^0.$$ 4. **Evaluate the zero exponent:** Any nonzero number raised to the zero power equals 1, so $$\left(-\frac{4}{11}\right)^0 = 1.$$ 5. **Final answer:** The value of the expression is **1**.