Simplify cube root of 2^4*5^5

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

Step 1

Raise $2$ to the power of $4$ .

$\sqrt[3]{16 \cdot 5^{5}}$

Step 2

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

$\sqrt[3]{16 \cdot 3125}$

Step 3

Multiply $16$ by $3125$ .

$\sqrt[3]{50000}$

Step 4

Rewrite $50000$ as $10^{3} \cdot 50$ .

Factor $1000$ out of $50000$ .

$\sqrt[3]{1000 (50)}$

Rewrite $1000$ as $10^{3}$ .

$\sqrt[3]{10^{3} \cdot 50}$

$\sqrt[3]{10^{3} \cdot 50}$

Step 5

Pull terms out from under the radical.

$10 \sqrt[3]{50}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt[3]{50}$

Decimal Form:

$36.84031498 \dots$

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