f) \( \sqrt{6^{4} \cdot 2^{4}} \)

To solve \( \sqrt{6^{4} \cdot 2^{4}} \), we can simplify it step-by-step. First, recognize that \( 6^{4} \) can be rewritten as \( (6^{2})^{2} \) and similarly for \( 2^{4} \). Now, notice that \( 6 = 2 \cdot 3 \). Thus, we can express it as \( \sqrt{(2 \cdot 3)^{4} \cdot 2^{4}} = \sqrt{2^{4} \cdot 3^{4} \cdot 2^{4}} = \sqrt{2^{8} \cdot 3^{4}} \). Using the property of square roots, we can take the square root of each factor: \( \sqrt{2^{8}} = 2^{4} \) and \( \sqrt{3^{4}} = 3^{2} \). Therefore, we get \( \sqrt{6^{4} \cdot 2^{4}} = 2^{4} \cdot 3^{2} \). Now, calculating those values gives us \( 2^{4} = 16 \) and \( 3^{2} = 9 \). Thus, multiplying them together gives us \( 16 \cdot 9 = 144 \). The final answer is \( 144 \).