1. **State the problem:** We need to find which expressions are equivalent to the given sums. 2. **First expression:** $10 + 5^4$ - Calculate $5^4 = 5 \times 5 \times 5 \times 5 = 625$ - So, $10 + 5^4 = 10 + 625 = 635$ 3. **Check each option for the first expression:** - 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 (correct) 4. **Second expression:** $1,000 + 196$ - Calculate sum: $1,000 + 196 = 1,196$ 5. **Check each option for the second expression:** - F: $10^2 + 7 \cdot 28 = 100 + 196 = 296$ (not equal to 1,196) - G: $10^3 + 14^2 = 1000 + 196 = 1,196$ (correct) - H: $100^3 + 7 \cdot 28 = 1,000,000 + 196 = 1,000,196$ (not equal to 1,196) - J: $100^2 + 14^2 = 10,000 + 196 = 10,196$ (not equal to 1,196) **Final answers:** - For $10 + 5^4$, the equivalent expression is D: None of these. - For $1,000 + 196$, the equivalent expression is G: $10^3 + 14^2$.