Simplify cube root of 40*(4 cube root of 5)

$\sqrt[3]{40} \cdot (4 \sqrt[3]{5})$

Step 1

Rewrite $40$ as $2^{3} \cdot 5$ .

Factor $8$ out of $40$ .

$\sqrt[3]{8 (5)} \cdot (4 \sqrt[3]{5})$

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

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

Step 2

Pull terms out from under the radical.

$2 \sqrt[3]{5} \cdot (4 \sqrt[3]{5})$

Step 3

Multiply $2 \sqrt[3]{5} (4 \sqrt[3]{5})$ .

Multiply $4$ by $2$ .

$8 \sqrt[3]{5} \sqrt[3]{5}$

Raise $\sqrt[3]{5}$ to the power of $1$ .

$8 ({\sqrt[3]{5}}^{1} \sqrt[3]{5})$

Raise $\sqrt[3]{5}$ to the power of $1$ .

$8 ({\sqrt[3]{5}}^{1} {\sqrt[3]{5}}^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 {\sqrt[3]{5}}^{1 + 1}$

Add $1$ and $1$ .

$8 {\sqrt[3]{5}}^{2}$

Step 4

Rewrite ${\sqrt[3]{5}}^{2}$ as $\sqrt[3]{5^{2}}$ .

$8 \sqrt[3]{5^{2}}$

Step 5

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

$8 \sqrt[3]{25}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt[3]{25}$

Decimal Form:

$23.39214190 \dots$