Evaluate -( sixth root of 64)^5

$- {(\sqrt[6]{64})}^{5}$

Rewrite $64$ as $2^{6}$ .

$- {\sqrt[6]{2^{6}}}^{5}$

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

$- 2^{5}$

Raise $2$ to the power of $5$ .

$- 1 \cdot 32$

Multiply $- 1$ by $32$ .

$- 32$

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