Thursday 22 January 2015

arithmetic - $(-32)^{frac{2}{10}}neq(-32)^{frac{1}{5}}$?

Is exponentiation by rational numbers defined only for simple fractions?



$(-32)^{\frac{2}{10}}=\sqrt[10]{(-32)^2}=\sqrt[10]{1024}=\pm2$ (and $8$ other complex roots)



$(-32)^{\frac{1}{5}}=\sqrt[5]{(-32)^1}=\sqrt[5]{-32}=-2$ (and $4$ other complex roots)




How do you settle this conflict?

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