1. **Stating the problem:** We are given two expressions: $$a = 10^2 + 10^{-2} + 10 + 10^{-1}$$ $$b = 10^2 \cdot 10 \cdot 10^{-2} \cdot 10^{-1}$$ We need to find the value of the product $a \cdot b$. 2. **Recall the rules:** - When multiplying powers of 10, add the exponents: $$10^m \cdot 10^n = 10^{m+n}$$ - When adding numbers, perform normal addition. 3. **Calculate $a$ step-by-step:** Calculate each term: - $10^2 = 100$ - $10^{-2} = 0.01$ - $10 = 10$ - $10^{-1} = 0.1$ Sum all terms: $$a = 100 + 0.01 + 10 + 0.1 = 110.11$$ 4. **Calculate $b$ step-by-step:** Multiply powers of 10 by adding exponents: $$b = 10^2 \cdot 10^1 \cdot 10^{-2} \cdot 10^{-1} = 10^{2+1-2-1} = 10^0 = 1$$ 5. **Calculate $a \cdot b$:** $$a \cdot b = 110.11 \cdot 1 = 110.11$$ **Final answer:** $110.11$ This corresponds to option C).