To simplify the expression $(a^4)(a^3)$, you apply the rule of exponents which states that when multiplying terms with the same base, you add their exponents:

$(a^4)(a^3) = a^{4+3} = a^7$

So, the simplified expression is:

$a^7$

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:

1. What is the result of $(b^5)(b^2)$?
2. How would you simplify $(x^3)(x^6)$?
3. What happens when you multiply $(a^2)(a^0)$?
4. How does the exponent rule apply to $(a^4)(a^{-2})$?
5. Can you simplify the expression $(a^5)(a^3)(a^2)$?

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