Final Answer:
The value of (-3/4)⁴ is 81/256.
Step-by-step explanation:
To calculate (-3/4)⁴, each factor is multiplied together. The numerator is raised to the fourth power, resulting in -3⁴, and the denominator is raised to the fourth power, resulting in 4⁴. The calculation is as follows:
![\[ (-3/4)⁴ = (-3)⁴ / 4⁴ = 81 / 256 \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/anebnxquewmwlpskngelcrser67vc4a4ut.png)
In this expression, the numerator, -3⁴, equals 81, and the denominator, 4⁴, equals 256. Therefore, the final answer is 81/256.
The negative exponent signifies that the result will be the reciprocal of the positive exponent. In this case, the reciprocal of (-3/4)⁴ is 4⁴/(-3)⁴, which simplifies to 256/81. However, since the original expression has a negative sign, the final answer is -81/256.
It's important to note that exponentiation indicates repeated multiplication. So, (-3/4)⁴ means multiplying (-3/4) by itself four times. The result, 81/256, reflects the product of these repeated multiplications.