1. **State the problem:** Simplify the expression $$2^{-4} \cdot 2^{-3}$$ using the properties of exponents. 2. **Recall the property of exponents:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the property:** $$2^{-4} \cdot 2^{-3} = 2^{-4 + (-3)} = 2^{-7}$$ 4. **Interpret the negative exponent:** A negative exponent means the reciprocal: $$2^{-7} = \frac{1}{2^7}$$ 5. **Calculate the value:** $$2^7 = 128$$ 6. **Final simplified expression:** $$\boxed{\frac{1}{128}}$$