1. **State the problem:** Evaluate the expression $$(2.5 \times 10^3) \times (3 \times 10^2)$$ and express the result in the form $[?] \times 10$. 2. **Recall the multiplication rule for powers of 10:** When multiplying powers of 10, add the exponents: $$10^a \times 10^b = 10^{a+b}$$. 3. **Multiply the coefficients:** Multiply the numbers 2.5 and 3: $$2.5 \times 3 = 7.5$$. 4. **Multiply the powers of 10:** Add the exponents of 10: $$10^3 \times 10^2 = 10^{3+2} = 10^5$$. 5. **Combine the results:** $$7.5 \times 10^5$$. 6. **Express in the form $[?] \times 10$:** Since $$7.5 \times 10^5 = 75 \times 10^4 = 750 \times 10^3 = 7500 \times 10^2 = 75000 \times 10^1$$, the expression can be written as $$75000 \times 10$$. **Final answer:** $$75000 \times 10$$.