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((2^5)/(2^frac (1)(2)))^(3)/(5)

Pergunta

((2^5)/(2^frac (1)(2)))^(3)/(5)

((2^5)/(2^frac (1)(2)))^(3)/(5)

Solução

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GilsonMestre · Tutor por 5 anos

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To simplify the expression \((\frac{2^5}{2^{\frac{1}{2}}})^{\frac{3}{5}}\), we can follow these steps:<br /><br />1. Simplify the fraction inside the parentheses:<br /> \[<br /> \frac{2^5}{2^{\frac{1}{2}}} = 2^{5 - \frac{1}{2}} = 2^{\frac{10}{2} - \frac{1}{2}} = 2^{\frac{9}{2}}<br /> \]<br /><br />2. Raise the result to the power of \(\frac{3}{5}\):<br /> \[<br /> (2^{\frac{9}{2}})^{\frac{3}{5}} = 2^{\frac{9}{2} \cdot \frac{3}{5}} = 2^{\frac{27}{10}}<br /> \]<br /><br />So, the simplified form of the given expression is:<br />\[<br />2^{\frac{27}{10}}<br />\]<br /><br />Therefore, the correct answer is:<br />\[<br />2^{\frac{27}{10}}<br />\]
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