1. **State the problem:** We are given the expression $A = 2^n \times 3 \times 5^m$ and asked to write $8A$ as a product of powers of its prime factors. 2. **Recall the formula and rules:** Multiplying powers with the same base means adding their exponents: $$a^x \times a^y = a^{x+y}$$ 3. **Express 8 as powers of primes:** Note that $8 = 2^3$. 4. **Multiply $8$ and $A$:** $$8A = 2^3 \times (2^n \times 3 \times 5^m)$$ 5. **Group like bases:** $$8A = 2^3 \times 2^n \times 3^1 \times 5^m$$ 6. **Add exponents for base 2:** $$8A = 2^{3+n} \times 3^1 \times 5^m$$ 7. **Final answer:** $$\boxed{8A = 2^{n+3} \times 3 \times 5^m}$$ This expresses $8A$ as a product of powers of its prime factors.