To check if 12^13-12^11-12^9 is divisible by 13, we can factor out the common factor of 12^9 from the expression:
12^13 - 12^11 - 12^9 = 12^9(12^4 - 12^2 - 1)
Now, we can apply the divisibility rule for 13. We need to multiply the last digit of 12^4 by 4 and add it to the rest of the number. If the outcome is divisible by 13, then the number is divisible by 13.
The last digit of 12^4 is 6. Therefore, we can calculate 6*4 + 1 = 25. Since 25 is not divisible by 13, 12^13 - 12^11 - 12^9 is not divisible by 13.