1. **State the problem:** Calculate the sum of $396$ and $8632643870438737723687327359735276336759912736387538975345$. 2. **Formula used:** Addition of two numbers is performed by adding their digits starting from the rightmost digit, carrying over any value greater than 9 to the next left digit. 3. **Perform the addition:** $$396 + 8632643870438737723687327359735276336759912736387538975345 = 8632643870438737723687327359735276336759912736387538975741$$ 4. **Explanation:** Since $396$ is much smaller than the large number, the addition affects only the last few digits of the large number. 5. **Final answer:** $$8632643870438737723687327359735276336759912736387538975741$$