1. **State the problem:** Calculate the value of the expression $$1 \cdot 2^{-2} + 1 \cdot 2^{-3} + 0 + 2^{-5} + 0 + 2^{-7} + 2^{-8}$$. 2. **Recall the rules:** - Negative exponents mean reciprocal powers: $$a^{-n} = \frac{1}{a^n}$$. - Powers of 2: $$2^{-2} = \frac{1}{2^2} = \frac{1}{4}$$, $$2^{-3} = \frac{1}{8}$$, etc. 3. **Calculate each term:** - $$1 \cdot 2^{-2} = \frac{1}{4} = 0.25$$ - $$1 \cdot 2^{-3} = \frac{1}{8} = 0.125$$ - $$0 = 0$$ - $$2^{-5} = \frac{1}{32} = 0.03125$$ - $$0 = 0$$ - $$2^{-7} = \frac{1}{128} = 0.0078125$$ - $$2^{-8} = \frac{1}{256} = 0.00390625$$ 4. **Sum all terms:** $$0.25 + 0.125 + 0 + 0.03125 + 0 + 0.0078125 + 0.00390625 = 0.41896875$$ 5. **Final answer:** $$\boxed{0.41896875}$$