5) \( \frac{3^{4}}{4^{4}} \)

To solve \( \frac{3^{4}}{4^{4}} \), let's first simplify it. We know that \( 4^{4} = (2^2)^{4} = 2^{8} \). So we can rewrite the expression as \( \frac{3^{4}}{2^{8}} \). Now, calculating \( 3^{4} = 81 \) and \( 2^{8} = 256 \), we have \( \frac{81}{256} \). This fraction is already in its simplest form, as 81 and 256 have no common factors. And there you have it! If you combine the powers, you could have an expression like \( \left( \frac{3}{4} \right)^{4} \) if you need it in a different format, which gives a neat little wrap to the solution.