Final answer:
The simplified expression for (-3c)^2 * a^-4 * b^0 is 9c^2/a^4. The exponent rules are applied: squared, negative exponent signifying reciprocal, and any nonzero number to the power of 0 equals 1. Option (b) is the correct choice.
Step-by-step explanation:
To find the simplified expression for (-3c)^2 * a^-4 * b^0, we can break it down into simpler parts and apply the laws of exponents.
- (-3c)^2 means (-3c) multiplied by itself, which is 9c^2 since (-3)^2 = 9 and (c)^2 = c^2.
- a^-4 is the reciprocal of a^4 because any negative exponent indicates that we should take the reciprocal of the base raised to the positive version of that exponent. Therefore, a^-4 is equivalent to 1/a^4.
- Any number (except for 0) raised to the 0th power is 1, so b^0 = 1.
Combining these results, we have 9c^2 multiplied by 1/a^4 multiplied by 1, which simplifies to 9c^2/a^4.
The presence of b^0 has no effect on the expression since it equals 1, and multiplying by 1 doesn't change the value of the expression.
Therefore, the correct simplified expression is 9c^2/a^4, and the correct option is (b).