Question

(Mackenzie) A raiz cúbica de 64^2 é :

a-) 4 raiz de 3 ^3
b-) 16
c-) 8
d-) 8 raiz de 2
e-) 1

estou com duvida

Answer 1

∛64² = ∛4096 = ∛16³ = 16 

Resposta letra b) 16

Answer 2

$\sqrt[b]{x^{a}}=x^{a/b}$ para $x,b~\textgreater~0$
_________________________

Vamos fatorar 64:

$64=2\cdot32=2\cdot(2\cdot16)=2\cdot(2\cdot16)=2^{2}\cdot(2\cdot8)=2^{3}\cdot2^{3}=2^{6}$

Então,

$64^{2}=(2^{6})^{2}=2^{6\cdot2}=2^{12}$

Portanto,

$\sqrt[3]{64^{2}}=\sqrt[3]{2^{12}}=2^{12/3}=2^{4}~~~\therefore~~\boxed{\boxed{\sqrt[3]{64^{2}}=16}}$