Simplify cube root of a( cube root of 2a^2+ cube root of 16a^2)

$\sqrt[3]{a} (\sqrt[3]{2 a^{2}} + \sqrt[3]{16 a^{2}})$

Step 1

Simplify each term.

Rewrite $16 a^{2}$ as $2^{3} \cdot (2 a^{2})$ .

Factor $8$ out of $16$ .

$\sqrt[3]{a} (\sqrt[3]{2 a^{2}} + \sqrt[3]{8 (2) a^{2}})$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Step 2

Simplify by adding terms.

Add $\sqrt[3]{2 a^{2}}$ and $2 \sqrt[3]{2 a^{2}}$ .

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

Rewrite using the commutative property of multiplication.

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

Step 3

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

Combine using the product rule for radicals.

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

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

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

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

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

Add $1$ and $2$ .

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

Step 4

Reorder $2$ and $a^{3}$ .

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

Step 5

Pull terms out from under the radical.

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