Final answer:
The simplified expression for (-3c)² * a⁻⁴ * b⁰ is 9c²a⁴, which corresponds to option A in the multiple-choice answers.
Step-by-step explanation:
To simplify the expression (-3c)² * a⁻⁴ * b⁰, we need to apply the rules of exponents. First, let's simplify each part of the expression:
- (-3c)²: When we square a negative number, the result is positive, and the variable c is also squared. Hence, (-3)² = 9 and c² remains as c², making this part of the expression 9c².
- a⁻⁴: A negative exponent denotes reciprocal. Therefore, a⁻⁴ is the same as 1/a⁴, but since we want to simplify, we can bring it to the numerator and change the sign of the exponent to positive, resulting in a⁴.
- b⁰: Any number (except 0) raised to the 0 power is 1. Hence, b⁰ becomes 1.
Putting it all together, we get 9c² * a⁴ * 1, which simplifies to 9c²a⁴ as the final expression.
Therefore, the answer is A) 9c²a⁴.