1. **Stating the problem:** Find the prime factorization of 350 and 200. 2. **Recall the prime factorization method:** Prime factorization means expressing a number as a product of prime numbers. 3. **Factorize 350:** Start dividing by the smallest prime numbers: $$350 \div 2 = 175$$ $$175 \div 5 = 35$$ $$35 \div 5 = 7$$ $$7 \div 7 = 1$$ So, the prime factors of 350 are: $$2 \times 5 \times 5 \times 7 = 2 \times 5^2 \times 7$$ 4. **Factorize 200:** $$200 \div 2 = 100$$ $$100 \div 2 = 50$$ $$50 \div 2 = 25$$ $$25 \div 5 = 5$$ $$5 \div 5 = 1$$ So, the prime factors of 200 are: $$2 \times 2 \times 2 \times 5 \times 5 = 2^3 \times 5^2$$ 5. **Match with the options:** 350 = $2 \times 5^2 \times 7$ 200 = $2^3 \times 5^2$ This corresponds to option (a): $2^3 \times 5^2$ and $2 \times 5^2 \times 7$ but reversed. Check carefully: Option (a) says 350 = $2^3 \times 5^2$ and 200 = $2 \times 5^2 \times 7$ which is incorrect. Option (d) says 350 = $2 \times 5^2 \times 7$ and 200 = $2^3 \times 5^2$ which matches our factorization. **Final answer:** (d) $2 \times 5^2 \times 7$ and $2^3 \times 5^2$