Simplify ( cube root of 4^5)( cube root of 5^5)

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

Step 1

Combine using the product rule for radicals.

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

Step 2

Simplify the expression.

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

$\sqrt[3]{1024 \cdot 5^{5}}$

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

$\sqrt[3]{1024 \cdot 3125}$

Multiply $1024$ by $3125$ .

$\sqrt[3]{3200000}$

$\sqrt[3]{3200000}$

Step 3

Rewrite $3200000$ as $40^{3} \cdot 50$ .

Factor $64000$ out of $3200000$ .

$\sqrt[3]{64000 (50)}$

Rewrite $64000$ as $40^{3}$ .

$\sqrt[3]{40^{3} \cdot 50}$

$\sqrt[3]{40^{3} \cdot 50}$

Step 4

Pull terms out from under the radical.

$40 \sqrt[3]{50}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$40 \sqrt[3]{50}$

Decimal Form:

$147.36125994 \dots$

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