We are asked to evaluate the expression $(\frac{5}{9})^7$.

1. Problem Description

We are asked to evaluate the expression $(\frac{5}{9})^7$.

2. Solution Steps

We need to raise the fraction $\frac{5}{9}$ to the power of

7. That means we need to raise both the numerator and the denominator to the power of

7. $(\frac{a}{b})^n = \frac{a^n}{b^n}$

So, we have:

$(\frac{5}{9})^7 = \frac{5^7}{9^7}$

$5^7 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 78125$

$9^7 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 = 4782969$

Therefore, $(\frac{5}{9})^7 = \frac{78125}{4782969}$

3. Final Answer

$\frac{78125}{4782969}$