Final answer:
Upon using exponent rules, the expression 3⁸ × (4²) × 4 / 12⁷ simplifies to 3/256, which equals 0.01171875. This answer does not correspond to any of the provided options, indicating a possible error in the question or answer choices.
Step-by-step explanation:
The question asks us to find the value of the expression 3⁸ × (4²) × 4 / 12⁷. We will use the properties of exponents to simplify the expression before performing the actual calculation. First, recognize that 12⁷ can be rewritten as (3 × 4)⁷ since 12 is the product of 3 and 4. Then the expression simplifies as follows:
- 3⁸ × (4²) × 4 / (3× 4)⁷ = 3⁸ × 4³ / 3⁷ × 4⁷
- Cancel out the common terms: 3⁸ / 3⁷ = 3, and 4³ / 4⁷ = 1/4⁴
- Therefore, the expression simplifies to 3 × 1/4⁴
- Calculating 4⁴ gives us 256, so the expression is 3/256
- Finally, dividing 3 by 256 gives us the decimal 0.01171875, which seems not to match any of the provided answer choices
Given that none of the provided answer choices match the calculation, there may be an error in the original question or the answer choices provided. Therefore, based on the calculation, the correct answer cannot be determined from the given options.