Final answer:
The expression -3⁴ results in -81, as only the value 3 is raised to the fourth power, and the negative sign is applied afterward, while the expression (-3)⁴ yields 81, since the negative base is raised to the fourth power, resulting in a positive value.
Step-by-step explanation:
When examining the expressions -3⁴ and (-3)⁴, it is essential to understand the role of parentheses and the effect they have on the calculation of the expression. The expression -3⁴ means that we should first consider the power of the number 3, which is 3 × 3 × 3 × 3, and then apply the negative sign, resulting in -81. In contrast, the expression (-3)⁴ indicates that the entire base, including the negative sign, is to be raised to the fourth power. As this involves multiplying a negative number by itself an even number of times, the result is a positive value: (-3) × (-3) × (-3) × (-3) = 81. Therefore, the correct answer is D. They differ in value but not in meaning.