Simplify the Radical Expression ( cube root of 24^4)/24

$\frac{\sqrt[3]{24^{4}}}{24}$

Step 1

Simplify the numerator.

Raise $24$ to the power of $4$ .

$\frac{\sqrt[3]{331776}}{24}$

Rewrite $331776$ as $48^{3} \cdot 3$ .

Factor $110592$ out of $331776$ .

$\frac{\sqrt[3]{110592 (3)}}{24}$

Rewrite $110592$ as $48^{3}$ .

$\frac{\sqrt[3]{48^{3} \cdot 3}}{24}$

$\frac{\sqrt[3]{48^{3} \cdot 3}}{24}$

Pull terms out from under the radical.

$\frac{48 \sqrt[3]{3}}{24}$

$\frac{48 \sqrt[3]{3}}{24}$

Step 2

Cancel the common factor of $48$ and $24$ .

Factor $24$ out of $48 \sqrt[3]{3}$ .

$\frac{24 (2 \sqrt[3]{3})}{24}$

Cancel the common factors.

Factor $24$ out of $24$ .

$\frac{24 (2 \sqrt[3]{3})}{24 (1)}$

Cancel the common factor.

$\frac{24 (2 \sqrt[3]{3})}{24 \cdot 1}$

Rewrite the expression.

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

Divide $2 \sqrt[3]{3}$ by $1$ .

$2 \sqrt[3]{3}$

$2 \sqrt[3]{3}$

$2 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{3}$

Decimal Form:

$2.88449914 \dots$

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