1. **State the problem:** Multiply the numbers $ (1 \times 10^4) \times (7 \times 10^4) $. 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. **Rewrite the expression:** $$ (1 \times 10^4) \times (7 \times 10^4) = 1 \times 7 \times 10^4 \times 10^4 $$ 4. **Multiply the coefficients:** $$ 1 \times 7 = 7 $$ 5. **Multiply the powers of 10 using the rule:** $$ 10^4 \times 10^4 = 10^{4+4} = 10^8 $$ 6. **Combine the results:** $$ 7 \times 10^8 $$ **Final answer:** $$7 \times 10^8$$