Simplify cube root of a( cube root of 5a^2+ cube root of 625a^2)

$\sqrt[3]{a} (\sqrt[3]{5 a^{2}} + \sqrt[3]{625 a^{2}})$

Simplify each term.

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Rewrite $625 a^{2}$ as $5^{3} \cdot (5 a^{2})$ .

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Factor $125$ out of $625$ .

$\sqrt[3]{a} (\sqrt[3]{5 a^{2}} + \sqrt[3]{125 (5) a^{2}})$

Rewrite $125$ as $5^{3}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Simplify by adding terms.

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

$\sqrt[3]{a} (6 \sqrt[3]{5 a^{2}})$

Rewrite using the commutative property of multiplication.

$6 \sqrt[3]{a} \sqrt[3]{5 a^{2}}$

Multiply $6 \sqrt[3]{a} \sqrt[3]{5 a^{2}}$ .

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Combine using the product rule for radicals.

$6 \sqrt[3]{5 a^{2} a}$

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

$6 \sqrt[3]{5 (a^{1} a^{2})}$

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

$6 \sqrt[3]{5 a^{1 + 2}}$

Add $1$ and $2$ .

$6 \sqrt[3]{5 a^{3}}$

Reorder $5$ and $a^{3}$ .

$6 \sqrt[3]{a^{3} \cdot 5}$

Pull terms out from under the radical.

$6 a \sqrt[3]{5}$

Simplify cube root of a( cube root of 5a^2+ cube root of 625a^2)

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