Simplify ( cube root of 5)^4

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

Rewrite ${\sqrt[3]{5}}^{4}$ as ${(5^{4})}^{\frac{1}{3}}$ .

$\sqrt[3]{5^{4}}$

Raise $5$ to the power of $4$ .

$\sqrt[3]{625}$

Rewrite $625$ as $5^{3} \cdot 5$ .

Factor $125$ out of $625$ .

$\sqrt[3]{125 (5)}$

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} \cdot 5}$

Pull terms out from under the radical.

$5 \sqrt[3]{5}$

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt[3]{5}$

Decimal Form:

$8.54987973 \dots$