Evaluate the Exponential Fraction: 2^9 ÷ 11^9

To solve this problem, we'll employ the exponent rules for fractions:

• Step 1: Recognize that $\frac{2^9}{11^9}$ follows the general form $\frac{a^n}{b^n}$.
• Step 2: Apply the property $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.
• Step 3: Substitute into the property to express the fraction as $\left(\frac{2}{11}\right)^9$.

Let's work through the steps in detail:

Step 1: The expression $\frac{2^9}{11^9}$ can be viewed as each number, 2 and 11, raised to the 9th power in a fraction.

Step 2: Utilize the exponent rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ to rewrite the fraction with a single power.

Step 3: Therefore, the expression $\frac{2^9}{11^9}$ simplifies to $\left(\frac{2}{11}\right)^9$.

Therefore, the correct answer is indeed $\left(\frac{2}{11}\right)^9$.

The correct choice from the provided options is:

$\left(\frac{2}{11}\right)^9$