Simplify ( cube root of 2^5)^(1/4)

${(\sqrt[3]{2^{5}})}^{\frac{1}{4}}$

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

${\sqrt[3]{32}}^{\frac{1}{4}}$

Rewrite $32$ as $2^{3} \cdot 4$ .

Factor $8$ out of $32$ .

${\sqrt[3]{8 (4)}}^{\frac{1}{4}}$

Rewrite $8$ as $2^{3}$ .

${\sqrt[3]{2^{3} \cdot 4}}^{\frac{1}{4}}$

${\sqrt[3]{2^{3} \cdot 4}}^{\frac{1}{4}}$

Pull terms out from under the radical.

${(2 \sqrt[3]{4})}^{\frac{1}{4}}$

Apply the product rule to $2 \sqrt[3]{4}$ .

$2^{\frac{1}{4}} {\sqrt[3]{4}}^{\frac{1}{4}}$

The result can be shown in multiple forms.

Exact Form:

$2^{\frac{1}{4}} {\sqrt[3]{4}}^{\frac{1}{4}}$

Decimal Form:

$1.33483985 \dots$

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