Calculate (5/8)^9: Evaluating a Fraction Raised to the Ninth Power

To solve this problem, we'll apply the rule for raising a fraction to a power:

Using the formula $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$, we can express $\left(\frac{5}{8}\right)^9$ as follows:

Step 1: Identify the base and exponent in $\left(\frac{5}{8}\right)^9$. Here, $a = 5$, $b = 8$, and $n = 9$.

Step 2: Apply the exponentiation rule:
$\left(\frac{5}{8}\right)^9 = \frac{5^9}{8^9}$.

Therefore, the original expression simplifies to $\frac{5^9}{8^9}$.

As a result, the correct rewritten form of $\left(\frac{5}{8}\right)^9$ is $\frac{5^9}{8^9}$.