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

Insert the corresponding expression:

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

Video Solution

Solution Steps

00:06 Let's simplify this problem together.

00:09 Remember, the law of exponents states that when a fraction is raised to a power like N,

00:14 both the numerator and the denominator need to be raised to the power of N.

00:20 We'll apply this rule to our exercise now.

00:23 First, calculate each power and then substitute the values in.

00:45 And that's how you find 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: $\frac{64}{125}$ .