Calculate (5×9÷20)³: Cube of a Fraction Problem

Question

$\left(\frac{5\times9}{20}\right)^3=$

00:00 Simplify the following problem

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

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

00:11 We will apply this formula to our exercise

00:15 Note that the numerator is a product, we must be careful with the parentheses

00:21 According to the laws of exponents, a product raised to a power (N)

00:25 equals the product broken down into factors with each factor raised to the power (N)

00:29 We will apply this formula to our exercise

00:37 This is the solution

To solve this problem, we'll follow these steps:

Now, let's work through each step:

Apply the power of a fraction rule:
$\frac{45^3}{20^3} = \frac{(5 \times 9)^3}{20^3} = \frac{5^3 \times 9^3}{20^3}$ .

Comparing this with the given choices, we find that:

The correct answer is Choice 1: $\frac{5^3 \times 9^3}{20^3}$ .

$\frac{5^3\times9^3}{20^3}$