Evaluate (5×9)/(8×10) Cubed: Complex Fraction Power Problem

To solve the problem $\left(\frac{5 \times 9}{8 \times 10}\right)^3$, we follow these steps:

• Step 1: Apply the exponent rule for fractions. According to the rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$, we apply the cube to both the numerator and the denominator.
• Step 2: Evaluate the numerator: $(5 \times 9)^3$.
• Step 3: Evaluate the denominator: $(8 \times 10)^3$.

Now, let's execute these steps:

First, simplify the expression by applying the cubed exponent:
$\left(\frac{5 \times 9}{8 \times 10}\right)^3 = \frac{(5 \times 9)^3}{(8 \times 10)^3}$

Next, use the exponential rule that states $(ab)^n = a^n \times b^n$:
For the numerator:
$(5 \times 9)^3 = 5^3 \times 9^3$

For the denominator:
$(8 \times 10)^3 = 8^3 \times 10^3$

Thus, the entire expression simplifies to:
$\frac{5^3 \times 9^3}{8^3 \times 10^3}$

The corresponding expression that matches this is, therefore,
$\frac{5^3 \times 9^3}{8^3 \times 10^3}$

Hence, the correct answer is $\frac{5^3 \times 9^3}{8^3 \times 10^3}$.