1. The problem is to express the number $\frac{5}{2} \times 3.54$ as a product of prime factors with positive exponents. 2. First, calculate the product: $$\frac{5}{2} \times 3.54 = \frac{5 \times 3.54}{2} = \frac{17.7}{2} = 8.85$$ 3. Now, express 8.85 as a fraction to factor it into primes. Since 8.85 = $\frac{885}{100}$, simplify the fraction: $$\frac{885}{100} = \frac{177}{20}$$ 4. Factor numerator and denominator into primes: - $177 = 3 \times 59$ (since 177 divided by 3 is 59, which is prime) - $20 = 2^2 \times 5$ 5. Therefore, $$8.85 = \frac{3 \times 59}{2^2 \times 5}$$ 6. This is the prime factorization with positive exponents for numerator and denominator. Final answer: $$8.85 = \frac{3^1 \times 59^1}{2^2 \times 5^1}$$