1. **State the problem:** Calculate the sum of $4.82 \times 10^4$ and $3.45 \times 10^4$. 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:** $$4.82 \times 10^4 + 3.45 \times 10^4 = (4.82 + 3.45) \times 10^4$$ $$= 8.27 \times 10^4$$ 4. **Explanation:** Since both terms have the same power of 10, we simply add the decimal parts $4.82$ and $3.45$ to get $8.27$, then multiply by $10^4$. 5. **Final answer:** $$8.27 \times 10^4$$