Final answer:
The simplified expression of 18a¹²C⁵ / 6a³ C² is 3a⁹C³, achieved by dividing the coefficients and subtracting the exponents of like variables.
Step-by-step explanation:
To simplify the expression 18a¹²C⁵ / 6a³ C², use the properties of exponents and division of polynomials. Divide the coefficients and subtract the exponents of like bases:
- Divide the coefficients: 18/6 = 3.
- For the variable 'a', subtract the exponents: 12 - 3 = 9, so a⁹.
- For the variable 'C', subtract the exponents: 5 - 2 = 3, so C³.
The simplified expression is 3a⁹C³, which corresponds to option A) 3a⁹C³.