Final answer:
To simplify the expression 3a^2b^-4/12a^-2b^-2, first, simplify the numerator and denominator separately by using the rules for exponents. Then, cancel out common factors. The simplified expression is 3/b^6.
Step-by-step explanation:
To simplify the expression 3a^2b^-4/12a^-2b^-2, we can first simplify the numerator and denominator separately.
In the numerator, we simplify a^2 to a * a and b^-4 to 1/b^4. So, the numerator becomes 3a * a * 1/b^4.
In the denominator, we simplify a^-2 to 1/a^2 and b^-2 to 1/b^2. So, the denominator becomes 12 * 1/a^2 * 1/b^2.
Now, we can simplify the expression by canceling out common factors. Canceling out a * an in the numerator and 1/a^2 in the denominator, we get 3/b^4 * 1/b^2.
Finally, multiplying the remaining terms, we get 3/b^6 as the simplified expression.