Calculate (3/2)³: Evaluating the Cube of a Fraction

Insert the corresponding expression:

$\left(\frac{3}{2}\right)^3=$

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)

00:08 equals the numerator and denominator raised to the same power (N)

00:11 We will apply this formula to our exercise

00:17 We'll calculate each power and substitute accordingly

00:36 This is the solution

Step-by-Step Solution

To solve $\left(\frac{3}{2}\right)^3$ , follow these steps:

Step 1: Identify the fraction to be raised to a power, $\frac{3}{2}$ , and the exponent, 3.
Step 2: Apply the power to both the numerator and the denominator separately using the exponent rule for fractions.

Let's evaluate:

Raise the numerator 3 to the power of 3:

$3^3 = 3 \times 3 \times 3 = 27$

Raise the denominator 2 to the power of 3:

$2^3 = 2 \times 2 \times 2 = 8$

Combine these results into the fraction $\frac{27}{8}$ .

Therefore, $\left(\frac{3}{2}\right)^3 = \frac{27}{8}$ .

Given several answer choices, the correct choice is 4: $\frac{27}{8}$ .