To simplify $(a^3)(a^5)$, you apply the rule of exponents which states that when multiplying powers with the same base, you add the exponents.

$(a^3)(a^5) = a^{3+5} = a^8$

Thus, $(a^3)(a^5)$ simplifies to $a^8$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you simplify $(a^2)(a^4)(a^3)$?
2. What is the result of $(x^5)(x^7)$?
3. How do you simplify $(b^6)(b^{-2})$?
4. What happens when you multiply powers with different bases?
5. How would you simplify $(m^3)(n^3)$?

Tip: When multiplying exponents with the same base, always remember to add the exponents!