Calculando-se (-1/243)^-2/5
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⇒![\sqrt[c]{a^b}=a^{\frac{b}{c}}](https://tex.z-dn.net/?f=%5Csqrt%5Bc%5D%7Ba%5Eb%7D%3Da%5E%7B%5Cfrac%7Bb%7D%7Bc%7D%7D "\sqrt[c]{a^b}=a^{\frac{b}{c}}")
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![\left(-\frac{1}{243}\right)^{-\frac{2}{5}}\\\left(-243\right)^{\frac{2}{5}}\\\sqrt[5]{\left(-243\right)^2}\\\sqrt[5]{243^2}\\\sqrt[5]{\left(3\cdot 3\cdot 3\cdot 3\cdot 3\right)^2}\\\sqrt[5]{\left(3^5\right)^2}\\\sqrt[5]{3^{10}}\\3^{\frac{10}{5}}\\3^2\\\boxed{\bold{9}}](https://tex.z-dn.net/?f=%5Cleft%28-%5Cfrac%7B1%7D%7B243%7D%5Cright%29%5E%7B-%5Cfrac%7B2%7D%7B5%7D%7D%5C%5C%5Cleft%28-243%5Cright%29%5E%7B%5Cfrac%7B2%7D%7B5%7D%7D%5C%5C%5Csqrt%5B5%5D%7B%5Cleft%28-243%5Cright%29%5E2%7D%5C%5C%5Csqrt%5B5%5D%7B243%5E2%7D%5C%5C%5Csqrt%5B5%5D%7B%5Cleft%283%5Ccdot+3%5Ccdot+3%5Ccdot+3%5Ccdot+3%5Cright%29%5E2%7D%5C%5C%5Csqrt%5B5%5D%7B%5Cleft%283%5E5%5Cright%29%5E2%7D%5C%5C%5Csqrt%5B5%5D%7B3%5E%7B10%7D%7D%5C%5C3%5E%7B%5Cfrac%7B10%7D%7B5%7D%7D%5C%5C3%5E2%5C%5C%5Cboxed%7B%5Cbold%7B9%7D%7D "\left(-\frac{1}{243}\right)^{-\frac{2}{5}}\\\left(-243\right)^{\frac{2}{5}}\\\sqrt[5]{\left(-243\right)^2}\\\sqrt[5]{243^2}\\\sqrt[5]{\left(3\cdot 3\cdot 3\cdot 3\cdot 3\right)^2}\\\sqrt[5]{\left(3^5\right)^2}\\\sqrt[5]{3^{10}}\\3^{\frac{10}{5}}\\3^2\\\boxed{\bold{9}}")
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