Mastering the Fraction: Simplify (3/7)^-9

To solve the problem, we will follow these steps:

• Step 1: Apply the negative exponent rule to rewrite the expression.
• Step 2: Use the power of a fraction rule to find the correct form.

Now, let's work through each step:
Step 1: The expression is $(\frac{3}{7})^{-9}$. Using the negative exponent rule, we can rewrite it as $\frac{1}{(\frac{3}{7})^{9}}$.

Step 2: By applying the power of a fraction rule, we find $\frac{1}{(\frac{3}{7})^{9}} = \frac{1}{\frac{3^9}{7^9}}$.
This expression can further be simplified to $\frac{7^9}{3^9}$ by inverting the fraction in the denominator.

Therefore, the solution to the problem is $\frac{7^9}{3^9}$.