Simplify cube root of 5a^2* cube root of 2a

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

Step 1

Multiply $\sqrt[3]{5 a^{2}} \sqrt[3]{2 a}$ .

Combine using the product rule for radicals.

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

Multiply $2$ by $5$ .

$\sqrt[3]{10 a^{2} a}$

Raise $a$ to the power of $1$ .

$\sqrt[3]{10 (a^{1} a^{2})}$

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

$\sqrt[3]{10 a^{1 + 2}}$

Add $1$ and $2$ .

$\sqrt[3]{10 a^{3}}$

Step 2

Reorder $10$ and $a^{3}$ .

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

Step 3

Pull terms out from under the radical.

$a \sqrt[3]{10}$