Question

como resolver
$\sqrt3 {}^{ - 3}$
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Answer 1

$\sqrt{3}^{-3}~=~\left(\frac{1}{\sqrt{3}}\right)^3~=~\left(\frac{1^3}{\sqrt{3}^3}\right)~=~\frac{1}{\sqrt{3}.\sqrt{3}.\sqrt{3}}~=~\frac{1}{\sqrt{3}^2.\sqrt{3}}~=~\boxed{\frac{1}{3.\sqrt{3}}}\\\\\\Podemos~ainda~racionalizar~a~fracao:\\\\\\\frac{1}{3\sqrt{3}}~.~\frac{\sqrt{3}}{\sqrt{3}}~=~\frac{1~.~\sqrt{3}}{3\sqrt{3}^2}~=~\frac{\sqrt{3}}{3~.~3}~=~\boxed{\frac{\sqrt{3}}{9}}$