Final answer:
The expression (3/4)⁴ is evaluated by multiplying the fraction by itself four times. After carrying out the multiplications, the result is 81/256, which is the simplest form of the fraction.
Step-by-step explanation:
To evaluate the expression (3/4)⁴, we need to adhere to the rules for multiplying fractions. When multiplying fractions, we multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
In this scenario, we have the fraction 3/4 multiplied by itself four times, which is (3/4) × (3/4) × (3/4) × (3/4). By performing the multiplication, we calculate 3× 3× 3× 3 in the numerator and 4× 4× 4× 4 in the denominator. This results in 81 over 256.
The fraction 81/256 is already in its simplest form since there are no common factors between 81 and 256 other than 1.
Therefore, the expression (3/4)⁴ evaluated as a fraction in simplest form is 81/256.