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

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

• Step 1: Evaluate the product in the numerator.

• Step 2: Apply the power of a fraction rule.

• Step 3: Simplify using the power of a product rule.

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: $\frac{5^3 \times 9^3}{20^3}$.