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Estudos Gerais04/10/2025

simplifique as potencias com expoentes fracionarios. a) 6^{...

simplifique as potencias com expoentes fracionarios. a) 6^{4/3} = \sqrt[3]{6^4} = 6^{4/3} = 6^{3/3} = 3^{3} = 9 b) 5^{3/2} = 5^{3/2} = \sqrt{5^3} = 5^{1.5} c) 3^{5/7} d) 4^{2/3} = \sqrt[3]{4^2} = \sqrt{(6^2)^2} \cdot \sqrt{5^2} = 5^{1} e) 4^{3/2} \sqrt{4^5} = \sqrt{2^2}^{3} = \sqrt{2^6} = \sqrt{2^2 \cdot 2^2 \cdot 2^2} 8

Como resolver

simplifique as potencias com expoentes fracionarios.
 a) 6^{4/3} = \sqrt[3]{6^4} = 6^{4/3} = 6^{3/3} = 3^{3} = 9
 b) 5^{3/2} = 5^{3/2} = \sqrt{5^3} = 5^{1.5}
 c) 3^{5/7}
 d) 4^{2/3} = \sqrt[3]{4^2} = \sqrt{(6^2)^2} \cdot \sqrt{5^2} = 5^{1}
 e) 4^{3/2} \sqrt{4^5} = \sqrt{2^2}^{3} = \sqrt{2^6} = \sqrt{2^2 \cdot 2^2 \cdot 2^2}
 8
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