D. 1/12^-4
Step-by-step explanation:
![12^{-5}*12^{9}](/tpl/images/2666/8133/0d50a.png)
Since both exponents have the same base, we can add the exponents to get:
![12^{-5+9}=12^{4}](/tpl/images/2666/8133/8e86c.png)
We can cross out A and B since they multiplied the two exponents, therefore both answers are wrong.
Now, let's try C and D.
C is wrong because it has a different base being raised to the same power.
D is correct. When you have a negative exponent, it is equivalent to the reciprocal of the base to the positive exponent.
The reciprocal of 1/12 is 12, and the positive of -4 is 4, therefore the answer is D.