1. **State the problem:** Calculate the sum of $3.4 \times 10^5$ and $5.3 \times 10^5$. 2. **Formula and rules:** When adding numbers in scientific notation with the same exponent, add the coefficients and keep the exponent the same. 3. **Intermediate work:** $$3.4 \times 10^5 + 5.3 \times 10^5 = (3.4 + 5.3) \times 10^5$$ $$= 8.7 \times 10^5$$ 4. **Explanation:** Since both terms have the same power of 10, we simply add the decimal parts 3.4 and 5.3 to get 8.7, then multiply by $10^5$. 5. **Final answer:** $$8.7 \times 10^5$$