simplify. rewrite the expression in the form $9^n$. \\(\\dfrac{9^{-3}}{9^{12}} = \\)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we subtract the exponents: $\frac{a^m}{a^n}=a^{m - n}$. Here, the base $a = 9$, $m=-3$, and $n = 12$.

Step2: Apply the exponent rule

Substitute the values into the rule: $9^{-3-12}$.

Step3: Simplify the exponent

Calculate $-3-12=-15$. So the expression becomes $9^{-15}$.

Answer:

$9^{-15}$