Final answer:
To evaluate (3/4) to the power of 4, multiply the fraction by itself four times: (3/4) × (3/4) × (3/4) × (3/4). This results in multiplying the numerators to get 81 and the denominators to get 256, so the answer is 81/256.
Step-by-step explanation:
Evaluating Powers of Fractions
To evaluate (3/4) to the power of 4, we simply multiply 3/4 by itself four times. The process is the same as with whole
numbers, where the expression nx means multiplying n by itself x times. Here's a step-by-step breakdown:
- Write out the expression: (3/4) × (3/4) × (3/4) × (3/4).
- Multiply the numerators together: 3 × 3 × 3 × 3 = 81.
- Multiply the denominators together: 4 × 4 × 4 × 4 = 256.
- Combine the two results: 81/256.
Therefore, (3/4) raised to the 4th power equals 81/256.