To simplify the expression \(\frac{x^{\frac{7}{9}}}{x^{\frac{5}{9}}}\), we can use the property of exponents that states:
\[ \frac{a^m}{a^n} = a^{m-n} \]
Applying this property to our expression:
\[ \frac{x^{\frac{7}{9}}}{x^{\frac{5}{9}}} = x^{\frac{7}{9} - \frac{5}{9}} \]
Now, we subtract the exponents:
\[ \frac{7}{9} - \frac{5}{9} = \frac{7 - 5}{9} = \frac{2}{9} \]
Therefore, we can simplify the expression to:
\[ x^{\frac{2}{9}} \]
So, the final simplified form is:
\[ \boxed{x^{\frac{2}{9}}} \]