Simplify ( cube root of -1)^0

${(\sqrt[3]{- 1})}^{0}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${\sqrt[3]{{(- 1)}^{3}}}^{0}$

Pull terms out from under the radical, assuming real numbers.

${(- 1)}^{0}$

Anything raised to $0$ is $1$ .

$1$

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