1. **Problem:** Calculate $$(4.2 \times 10^4) \times (2 \times 10^3)$$ and write the answer in standard form. 2. **Formula:** When multiplying numbers in scientific notation, multiply the coefficients and add the exponents: $$a \times 10^m \times b \times 10^n = (a \times b) \times 10^{m+n}$$ 3. **Calculation:** $$4.2 \times 2 = 8.4$$ $$10^{4+3} = 10^7$$ 4. **Combine:** $$8.4 \times 10^7$$ 5. **Convert to standard form:** $$8.4 \times 10^7 = 84000000$$ **Final answer:** 84000000