1. **Problem:** Calculate the value of the expression $2\cdot 2^{2026} + 3\cdot 2^{2027}$ and identify which option (a-f) it equals. 2. **Formula and rules:** Use properties of exponents: $a^m \cdot a^n = a^{m+n}$ and factor common terms. 3. **Intermediate work:** $$2\cdot 2^{2026} + 3\cdot 2^{2027} = 2^{1} \cdot 2^{2026} + 3 \cdot 2^{2027} = 2^{2027} + 3 \cdot 2^{2027}$$ 4. Factor out $2^{2027}$: $$2^{2027} + 3 \cdot 2^{2027} = (1 + 3) \cdot 2^{2027} = 4 \cdot 2^{2027}$$ 5. Simplify: $$4 \cdot 2^{2027} = 2^{2} \cdot 2^{2027} = 2^{2029}$$ 6. **Answer:** The expression equals $2^{2029}$, which corresponds to option (a). **Final answer:** a