Question

por que a raiz de quinto de 512 equivale a 2 raiz do quinto de 16??

Answer 1

Resposta:

512^(1/5) = (2^9)^(1/5)  = 2^(9/5)

2 * 16^(1/5) =2 *(2^4)^(1/5 ) = 2*2^(4/5) =2^(1+4/5) =2^(5/5+4/5)=2^(9/5)

512^(1/5) =  2 * 16^(1/5)

Answer 2

Resposta:

$\sqrt[5]{512} =\sqrt[5]{2^9} =\sqrt[5]{2^5.2^4} =\sqrt[5]{2^5} .\sqrt[5]{2^4} =2\sqrt[5]{16} \\ \\ logo\\ \\ \sqrt[5]{512} =2\sqrt[5]{16}$

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fatorando 512

512 | 2

256 | 2

128 | 2

 64 | 2

 32 | 2

 16 | 2

   8 | 2

   4 | 2

   2 | 2

   1