Question

³√2⁵√8/¹⁵√1/128
a) 1
b) 2​

Answer 1

• Uma fração com raiz é calculada da mesma forma que calculamos uma raiz comum.

• Vamos lá

$\sf \displaystyle \large{\frac{\sqrt[\sf 3]{\sf 2\sqrt[\sf 5]{\sf 8}}}{\sqrt[\sf 15]{\frac{\sf 1}{\sf 128}}}}\\\\\\\sf\large{\sqrt[\sf 15]{\sf \frac{1}{128} } }=\large{\frac{1}{\sqrt[\sf 15]{\sf 128 } }$

$\sf \displaystyle \large{\frac{\sqrt[\sf 3]{\sf 2\sqrt[\sf 5]{\sf 8}}}{\dfrac{1}{\sqrt[\sf 15]{\sf 128}}}}\\\\\\\sf \large{\frac{2^{\frac{\large{8}\sf }{\sf 15}}}{\dfrac{1}{\sqrt[\sf15]{\sf 128}}}}\\\\\\\sf Lembre \ de \ aplicar \ a \ propriedade \ de \iff \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}$

$\sf \displaystyle \large{\dfrac{2^{\frac{8}{15}}\sqrt[\sf 15]{\sf 128}}{1}}\\\\\\\sf \:regra\:\frac{a}{1}=a\\\\\\\sf \large{2^{\frac{8}{15}}\sqrt[\sf 15]{\sf 128}}\\\\\\\sf \large{2^{\frac{8}{15}}\sqrt[\sf 15]{\sf 2^7}}\\\\\\\sf \sf Aplique \ a \ Propriedade \ dos \ expoentes \to \left(a^b\right)^c=a^{bc}\\\\\\\sf 2^{\frac{8}{15}}\cdot \:2^{7\cdot \frac{1}{15}}\\\\\\2^{\frac{8}{15}}\cdot \:2^{\frac{7}{15}}\\\\\\\sf 2^{\frac{8}{15}+\frac{7}{15}}\\\\\\\sf 2^1\\\\\\Regra ~a^1=a$

$\boxed{\boxed{\sf\large{ S=\{ 2 \}}}}$

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