1. **State the problem:** Complete the prime factor trees for the given numbers. 2. **Recall the prime factorization rule:** Every composite number can be expressed as a product of prime numbers. 3. **Prime factorization of each number:** - For 16: $$16 = 2 \times 8 = 2 \times (2 \times 4) = 2 \times 2 \times (2 \times 2) = 2^4$$ - For 42: $$42 = 2 \times 21 = 2 \times (3 \times 7) = 2 \times 3 \times 7$$ - For 40: $$40 = 2 \times 20 = 2 \times (2 \times 10) = 2 \times 2 \times (2 \times 5) = 2^3 \times 5$$ - For 24: $$24 = 8 \times 3 = (2 \times 4) \times 3 = (2 \times (2 \times 2)) \times 3 = 2^3 \times 3$$ - For 18: $$18 = 2 \times 9 = 2 \times (3 \times 3) = 2 \times 3^2$$ - For 50: $$50 = 5 \times 10 = 5 \times (2 \times 5) = 2 \times 5^2$$ 4. **Explanation:** Each number is broken down into two factors repeatedly until all factors are prime numbers. 5. **Final prime factorizations:** - 16 = $2^4$ - 42 = $2 \times 3 \times 7$ - 40 = $2^3 \times 5$ - 24 = $2^3 \times 3$ - 18 = $2 \times 3^2$ - 50 = $2 \times 5^2$