Simplify ( cube root of 256)^4

${(\sqrt[3]{256})}^{4}$

Rewrite $256$ as $4^{3} \cdot 4$ .

Factor $64$ out of $256$ .

${\sqrt[3]{64 (4)}}^{4}$

Rewrite $64$ as $4^{3}$ .

${\sqrt[3]{4^{3} \cdot 4}}^{4}$

Pull terms out from under the radical.

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

Simplify the expression.

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

$4^{4} {\sqrt[3]{4}}^{4}$

Raise $4$ to the power of $4$ .

$256 {\sqrt[3]{4}}^{4}$

Rewrite ${\sqrt[3]{4}}^{4}$ as ${(4^{4})}^{\frac{1}{3}}$ .

$256 \sqrt[3]{4^{4}}$

Raise $4$ to the power of $4$ .

$256 \sqrt[3]{256}$

Rewrite $256$ as $4^{3} \cdot 4$ .

Factor $64$ out of $256$ .

$256 \sqrt[3]{64 (4)}$

Rewrite $64$ as $4^{3}$ .

$256 \sqrt[3]{4^{3} \cdot 4}$

Pull terms out from under the radical.

$256 (4 \sqrt[3]{4})$

Multiply $4$ by $256$ .

$1024 \sqrt[3]{4}$

The result can be shown in multiple forms.

Exact Form:

$1024 \sqrt[3]{4}$

Decimal Form:

$1625.49867721 \dots$