To simplify the expression $(9^{-3})(9^{12})$, we can use the product of powers property of exponents. This property states that when multiplying two powers with the same base, you add the exponents:

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

For our expression:

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

Thus, the simplified expression is:

$9^9$

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Would you like more details on exponent rules, or do you have any further questions about this? Here are some related questions:

1. What is the value of $9^9$?
2. How do you handle negative exponents in expressions?
3. Can you explain how to simplify powers of 10 in a similar way?
4. What happens when you divide powers with the same base?
5. How do you simplify expressions involving fractional exponents?

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