To evaluate \((\frac{3}{4})^{-2}\), we can use the property of exponents that states \(a^{-n} = \frac{1}{a^n}\). Therefore:
\[ (\frac{3}{4})^{-2} = \frac{1}{(\frac{3}{4})^2} \]
Next, we calculate \((\frac{3}{4})^2\):
\[ (\frac{3}{4})^2 = \frac{3^2}{4^2} = \frac{9}{16} \]
Now we plug this back into our expression:
\[ (\frac{3}{4})^{-2} = \frac{1}{\frac{9}{16}} = \frac{16}{9} \]
Thus, the value of \((\frac{3}{4})^{-2}\) is:
\[ \boxed{\frac{16}{9}} \]