Answer
$\frac{1}{3}$
Work Step by Step
We know that $b^{-n}=\frac{1}{b^{n}}$ (where $b$ is a nonzero real number and $n$ is a natural number).
Therefore, $27^{-\frac{1}{3}}=\frac{1}{27^{\frac{1}{3}}}$
Based on the definition of $a^{\frac{m}{n}}$, we know that $a^{\frac{m}{n}}=(\sqrt[n] a)^{m}=\sqrt[n] a^{m}$ (where $\sqrt[n] a$ is a real number).
Therefore, $\frac{1}{27^{\frac{1}{3}}}=\frac{1}{\sqrt[3] 27^{1}}=\frac{1}{\sqrt[3] 27}=\frac{1}{3}$
We know that $\sqrt[3] 27=3$, because $3^{3}=27$.
