Simplify (x/y)^8: Evaluating Powers of Fractional Expressions

To solve this problem, we will apply the power of a fraction rule:

Step 1: Recognize that we are asked to simplify $\left(\frac{x}{y}\right)^8$.

Step 2: Apply the power of a fraction rule, which states:

• $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$

Step 3: Use this formula to obtain:

$\left(\frac{x}{y}\right)^8 = \frac{x^8}{y^8}$

Therefore, the simplified expression of $\left(\frac{x}{y}\right)^8$ is $\frac{x^8}{y^8}$.

The correct choice from the given options is:

$\frac{x^8}{y^8}$