Calculate (4/5)³: Evaluating the Cube of a Fraction

To solve this problem, we will evaluate the expression $\left(\frac{4}{5}\right)^3$ following these steps:

• Step 1: Apply the power to the numerator.
• Step 2: Apply the power to the denominator.
• Step 3: Calculate the results for both and simplify if possible.

Let's go through each step:

Step 1: Calculate the cube of the numerator, which is 4. That is, $4^3 = 4 \times 4 \times 4 = 64$.

Step 2: Calculate the cube of the denominator, which is 5. That is, $5^3 = 5 \times 5 \times 5 = 125$.

Step 3: Combine these results into a fraction: $\frac{64}{125}$.

Therefore, the expression $\left(\frac{4}{5}\right)^3$ simplifies to $\frac{64}{125}$.

Upon comparing with the given choices, the correct answer is choice 1: $\frac{64}{125}$.