Question

utilizando as propriedades transforme as expressões em um único radical

Answer 1

a) $\sqrt[6]{ \frac{5}{3} } * \sqrt[6]{12} = \sqrt[6]{ \frac{5*12}{3} } = \sqrt[6]{ \frac{60}{3} } = \sqrt[6]{20}$

b) $\frac{ \sqrt[7]{ \sqrt[]{22}} }{ \sqrt[14]{2} } = \frac{ \sqrt[7]{ 22^{ \frac{1}{2} } } }{ \sqrt[14]{2} } = \frac{( 22^{ \frac{1}{2} } )^{ \frac{1}{7} } }{ 2^{ \frac{1}{14} } } = \frac{ 22^{ \frac{1}{2}* \frac{1}{7} }}{2^{ \frac{1}{14} } }= \frac{ 22^{ \frac{1}{14} } }{ 2^{ \frac{1}{14} } } = \sqrt[14]{ \frac{22}{2} } = \sqrt[14]{ 11}$

c) $\frac{ \sqrt[12]{5} }{ \sqrt[12]{4} } * \sqrt[4]{ \sqrt[3]{6} } = \sqrt[12]{ \frac{5}{4} } *( 6^{ \frac{1}{3} } )^{ \frac{1}{4} } = \sqrt[12]{ \frac{5}{4} } * 6^{ \frac{1}{12} } = \sqrt[12]{ \frac{5}{4} } * \sqrt[12]{6} = \sqrt[12]{ \frac{5*6}{4} } \\ \\ =\sqrt[12]{ \frac{30}{4} } = \sqrt[12]{ \frac{15}{2} }$

d) $\sqrt[8]{15} * \frac{ \sqrt{ \sqrt{ \sqrt{4} } } }{ \sqrt{ \sqrt[4]{20} } } = \sqrt[8]{15} * \frac{(( 4^{1/2} )^{1/2})^{1/2} }{ (20^{1/4})^{1/2} } = \sqrt[8]{15} * \frac{ 4^{1/8} }{20^{1/8} } = \sqrt[8]{15} * \frac{ \sqrt[8]{4} }{ \sqrt[8]{20} } \\ \\ = \sqrt[8]{15} * \sqrt[8]{ \frac{4}{20} } = \sqrt[8]{ \frac{15*4}{8} } *= \sqrt[8]{ \frac{60}{20} } = \sqrt[8]{3}$

Pronto boa sorte.

Answer 2

Resposta:

Explicação passo-a-passo:

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