Final answer:
To simplify (c^3d^4)^3, multiply each exponent by 3, resulting in c^9 and d^12. The simplified expression is c^9d^12. The correct answer is option a.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on the cubing of exponentials which is a concept usually covered in middle school algebra. To simplify (c^3d^4)^3, we apply the rule that when raising a power to a power, you multiply the exponents.
Thus, the exponent of c is multiplied by 3 (3 × 3), and the same for d (4 × 3). Here's the step-by-step process: Identify the base numbers, which are c and d with their respective exponents of 3 and 4. Multiply each exponent by 3, since the entire expression is raised to the power of 3.
Simplifying, we get c^(3×3) and d^(4×3), which is c^9 and d^12, respectively. Combine the simplified expressions to get c^9d^12. Therefore, the simplified form of the original expression (c^3d^4)^3 is c^9d^12, which corresponds to option (a).