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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