1. **State the problem:** Calculate the product of $3.2 \times 10^5$ and $2 \times 10^9$ and write the answer in scientific notation. 2. **Recall the rule for multiplying numbers in scientific notation:** $$ (a \times 10^m)(b \times 10^n) = (a \times b) \times 10^{m+n} $$ where $a$ and $b$ are numbers, and $m$ and $n$ are exponents. 3. **Multiply the coefficients:** $$ 3.2 \times 2 = 6.4 $$ 4. **Add the exponents:** $$ 5 + 9 = 14 $$ 5. **Combine the results:** $$ (3.2 \times 10^5)(2 \times 10^9) = 6.4 \times 10^{14} $$ 6. **Final answer:** $$ \boxed{6.4 \times 10^{14}} $$