1. **State the problem:** Calculate $ (8 \times 10^2) \times (4 \times 10^6) $ and express the answer in standard form. 2. **Recall the rule for multiplying numbers in scientific notation:** $$ (a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m+n} $$ 3. **Apply the rule:** $$ (8 \times 10^2) \times (4 \times 10^6) = (8 \times 4) \times 10^{2+6} $$ 4. **Calculate the multiplication and addition of exponents:** $$ 8 \times 4 = 32 $$ $$ 2 + 6 = 8 $$ So, $$ 32 \times 10^8 $$ 5. **Convert to standard form:** Standard form requires the coefficient to be between 1 and 10. $$ 32 = 3.2 \times 10^1 $$ Therefore, $$ 32 \times 10^8 = (3.2 \times 10^1) \times 10^8 = 3.2 \times 10^{1+8} = 3.2 \times 10^9 $$ **Final answer:** $$ \boxed{3.2 \times 10^9} $$