1. **Stating the problems:** - Problem 1: Find the value equivalent to the expression shown (options: 19, -11, 7, -14). - Problem 2: Find the expression equivalent to $10 + 5^4$ (options: $10 + 5 \cdot 4$, $(10 + 5)^4$, $(10 + 5) \cdot 4$, None). - Problem 3: Find the expression equivalent to $1,000 + 196$ (options: $10^2 + 7 \cdot 28$, $10^3 + 14^2$). 2. **Problem 1 solution:** - From the handwritten work, $5^2 = 25$ and $25 - 34 = -9$. - The options given are 19, -11, 7, -14. - The handwritten work shows $25 - 34 = -9$ and $-11 - (-3) = -14$. - The value equivalent to the expression is $-14$. 3. **Problem 2 solution:** - Expression: $10 + 5^4$. - Calculate $5^4 = 5 \times 5 \times 5 \times 5 = 625$. - So, $10 + 5^4 = 10 + 625 = 635$. - Check options: - A: $10 + 5 \cdot 4 = 10 + 20 = 30$ (not equal to 635). - B: $(10 + 5)^4 = 15^4 = 50625$ (not equal to 635). - C: $(10 + 5) \cdot 4 = 15 \cdot 4 = 60$ (not equal to 635). - D: None of these. - Therefore, the equivalent expression is option D. 4. **Problem 3 solution:** - Expression: $1,000 + 196$. - Calculate $1,000 + 196 = 1196$. - Check options: - F: $10^2 + 7 \cdot 28 = 100 + 196 = 296$ (not equal to 1196). - G: $10^3 + 14^2 = 1000 + 196 = 1196$ (equal to the expression). - Therefore, the equivalent expression is option G. **Final answers:** - Problem 1: $-14$ - Problem 2: None of these - Problem 3: $10^3 + 14^2$