Final answer:
The Greatest Common Factor (GCF) of c⁴ d⁹ and c² d¹² is c² d⁹, which includes the smallest exponents of both variables present in the two expressions.
Step-by-step explanation:
The Greatest Common Factor (GCF) of c⁴ d⁹ and c² d¹² is found by identifying the highest powers of c and d that are common to both expressions. Since the exponents of c in c⁴ and c² are 4 and 2 respectively, the GCF will include the smaller exponent of c, which is 2. Similarly, for d in d⁹ and d¹² the smaller exponent is 9. Therefore, the GCF of c⁴ d⁹ and c² d¹² is c² d⁹.