1. The problem asks us to evaluate the expression $$(3.4 \times 10^2) \times (2 \times 10^3)$$ and express the result in the form $a \times 10^b$. 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 this rule to the given expression: $$ (3.4 \times 10^2) \times (2 \times 10^3) = (3.4 \times 2) \times 10^{2+3} $$ 4. Multiply the decimal numbers: $$ 3.4 \times 2 = 6.8 $$ 5. Add the exponents of 10: $$ 2 + 3 = 5 $$ 6. Combine the results: $$ 6.8 \times 10^5 $$ 7. Therefore, the expression evaluates to $6.8 \times 10^5$. Final answer: $6.8 \times 10^5$