1. **Stating the problem:** Simplify the expression $$\frac{2^{-3} \times 2^{5} \times 2^{0}}{2^{6} \times 2^{-3}}$$. 2. **Formula used:** When multiplying powers with the same base, add the exponents: $$a^{m} \times a^{n} = a^{m+n}$$. When dividing powers with the same base, subtract the exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$. 3. **Apply multiplication in numerator:** $$2^{-3} \times 2^{5} \times 2^{0} = 2^{-3+5+0} = 2^{2}$$ 4. **Apply multiplication in denominator:** $$2^{6} \times 2^{-3} = 2^{6 + (-3)} = 2^{3}$$ 5. **Divide numerator by denominator:** $$\frac{2^{2}}{2^{3}} = 2^{2-3} = 2^{-1}$$ 6. **Interpret negative exponent:** $$2^{-1} = \frac{1}{2^{1}} = \frac{1}{2}$$ **Final answer:** $$\frac{1}{2}$$