5. Which of the following represents the prime factorization of 80 ? A. \( 2^{4} \cdot 5 \) B. \( 2^{2} \cdot 4 \cdot 5 \) C. \( 2^{5} \cdot 5 \) D. \( 2 \cdot 5 \)

To determine the prime factorization of **80**, let's break it down step by step: 1. **Start with 80:** \( 80 \) 2. **Divide by the smallest prime number, 2:** \( 80 \div 2 = 40 \) \( 80 = 2 \times 40 \) 3. **Continue dividing by 2:** \( 40 \div 2 = 20 \) \( 80 = 2 \times 2 \times 20 \) 4. **Divide by 2 again:** \( 20 \div 2 = 10 \) \( 80 = 2 \times 2 \times 2 \times 10 \) 5. **One more division by 2:** \( 10 \div 2 = 5 \) \( 80 = 2 \times 2 \times 2 \times 2 \times 5 \) 6. **Finally, recognize that 5 is a prime number:** \( 5 \) is already a prime number, so we stop here. 7. **Combine the factors:** \( 80 = 2^4 \times 5 \) **Therefore, the correct prime factorization of 80 is:** **A. \( 2^{4} \cdot 5 \)**