Question

$\sqrt[3]{3} ^{1/3} =x$ qual o valor de x?

Answer 1

$x=(\sqrt[3]{3})^{\frac{1}{3}}$

Observe que, $a^{\frac{b}{c}}=\sqrt[c]{a^b}$.

Assim, $x=(\sqrt[3]{3})^{\frac{1}{3}}=\sqrt[3]{\sqrt[3]{3}}$.

Note que, $\sqrt[m]{\sqrt[n]{a}}=\sqrt[m\cdot n]{a}$.

Logo, $x=\sqrt[3]{\sqrt[3]{3}}=\sqrt[3\cdot3]{3}~\Rightarrow~\boxed{x=\sqrt[9]{3}}$.

Answer 2

$\boxed{( \sqrt[3]{3} )^\frac{1}{3}= \sqrt[3]{ \sqrt[3]{3} } }$

Usando a seguinte propriedade dos radicais:

$\boxed{ \sqrt[n]{ \sqrt[m]{a} } = \sqrt[mn]{a} }$

temos:

$\boxed{ \sqrt[3]{ \sqrt[3]{3} } = \sqrt[3.3]{3} = \sqrt[9]{3} }$