Evaluate (11×5×4)/(9×13×17) Raised to the Eighth Power

To solve the problem, follow these steps:

• Step 1: Use the property $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ to distribute the exponent 8 to both the numerator and the denominator.
  
• Step 2: Raise each component in the numerator and the denominator to the power of 8.

Start by applying the rule to the entire fraction:

$\left(\frac{11\times5\times4}{9\times13\times17}\right)^8 = \frac{(11\times5\times4)^8}{(9\times13\times17)^8}$

Then apply the rule of powers to the product inside both the numerator and denominator:

$= \frac{11^8 \times 5^8 \times 4^8}{9^8 \times 13^8 \times 17^8}$

Therefore, the solution to the given problem is:

$\frac{11^8\times5^8\times4^8}{9^8\times13^8\times17^8}$