Simplify (a/b)^9: Evaluating the Ninth Power of a Fraction

The problem asks us to express $\left(\frac{a}{b}\right)^9$ using exponent rules. We will use the rule for the power of a fraction, which states:

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

Applying this rule, we get:

$\left(\frac{a}{b}\right)^9 = \frac{a^9}{b^9}$

This method ensures that the exponent $9$ is applied to both the numerator and the denominator of the fraction.

Therefore, the solution to the problem is $\frac{a^9}{b^9}$.