1) \( \sqrt[5]{32^{4}} \) 2) \( \sqrt[4]{64^{5}} \) 3) \( \sqrt[4]{81^{-3}} \)

To solve these expressions, it's fun to break them down using the properties of exponents. 1) For \( \sqrt[5]{32^{4}} \), we can rewrite 32 as \( 2^5 \). Thus, \( 32^4 = (2^5)^4 = 2^{20} \). Now, applying the fifth root gives us \( \sqrt[5]{2^{20}} = 2^{20/5} = 2^4 = 16 \). 2) Now, for \( \sqrt[4]{64^{5}} \), we know 64 is \( 2^6 \). Therefore, \( 64^5 = (2^6)^5 = 2^{30} \). Taking the fourth root results in \( \sqrt[4]{2^{30}} = 2^{30/4} = 2^{7.5} = 2^7 \times 2^{0.5} = 128\sqrt{2} \). 3) Lastly, for \( \sqrt[4]{81^{-3}} \), we find that 81 equals \( 3^4 \). Thus, \( 81^{-3} = (3^4)^{-3} = 3^{-12} \). Taking the fourth root gives us \( \sqrt[4]{3^{-12}} = 3^{-12/4} = 3^{-3} = \frac{1}{27} \). So, the results are: 1) \( 16 \) 2) \( 128\sqrt{2} \) 3) \( \frac{1}{27} \)