The given expression is:

$(9^{-3})(9^{12})$

To simplify, you can apply the Product of Powers property, which states:

$a^m \cdot a^n = a^{m+n}$

So, for the given expression:

$9^{-3} \cdot 9^{12} = 9^{-3 + 12} = 9^9$

Thus, the simplified result is:

$9^9$

Would you like any further details or explanations?

Here are some related questions to expand on this topic:

1. How would you simplify $(5^4)(5^{-2})$?
2. What is the value of $9^9$?
3. Can you explain the quotient rule for exponents using an example?
4. How do you simplify expressions with different bases, like $3^2 \times 9^2$?
5. What happens if the exponents in the product rule are negative?

Tip: Always combine the exponents first when multiplying powers with the same base to simplify the expression efficiently.