1. The problem is to find the product of the numbers given: $2^2 \cdot 3 \cdot 5$. 2. The expression uses exponents and multiplication. Recall that $2^2$ means $2 \times 2$. 3. Calculate $2^2$ first: $$2^2 = 2 \times 2 = 4$$ 4. Now multiply the results step-by-step: $$4 \cdot 3 = 12$$ 5. Finally multiply by 5: $$12 \cdot 5 = 60$$ 6. So, the value of $2^2 \cdot 3 \cdot 5$ is $60$. 7. The prime factorization is already given as $2^2 \cdot 3 \cdot 5$ which is the product of primes 2, 3, and 5. Final answer: $60$