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

Insert the corresponding expression:

$\left(\frac{4}{5}\right)^3=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, a fraction raised to a power (N)

00:07 equals the numerator and denominator raised to the same power(N)

00:11 We will apply this formula to our exercise

00:16 Let's calculate each power and substitute accordingly

00:39 This is the solution

Step-by-Step Solution

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

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: $\frac{64}{125}$ .