Basic Math Examples

$3 b^{2} (\sqrt[3]{54 a}) + 3 (\sqrt[3]{2 a b^{6}})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $54 a$ as $3^{3} \cdot (2 a)$ .

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Step 1.1.1

Factor $27$ out of $54$ .

$3 b^{2} \sqrt[3]{27 (2) a} + 3 (\sqrt[3]{2 a b^{6}})$

Step 1.1.2

Rewrite $27$ as $3^{3}$ .

$3 b^{2} \sqrt[3]{3^{3} \cdot 2 a} + 3 (\sqrt[3]{2 a b^{6}})$

Step 1.1.3

Add parentheses.

$3 b^{2} \sqrt[3]{3^{3} \cdot (2 a)} + 3 (\sqrt[3]{2 a b^{6}})$

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $3$ by $3$ .

$9 b^{2} \sqrt[3]{2 a} + 3 (\sqrt[3]{2 a b^{6}})$

Step 1.4

Rewrite $2 a b^{6}$ as ${(b^{2})}^{3} \cdot (2 a)$ .

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Step 1.4.1

Rewrite $b^{6}$ as ${(b^{2})}^{3}$ .

$9 b^{2} \sqrt[3]{2 a} + 3 \sqrt[3]{2 a {(b^{2})}^{3}}$

Step 1.4.2

Move $a$ .

$9 b^{2} \sqrt[3]{2 a} + 3 \sqrt[3]{2 {(b^{2})}^{3} a}$

Step 1.4.3

Reorder $2$ and ${(b^{2})}^{3}$ .

$9 b^{2} \sqrt[3]{2 a} + 3 \sqrt[3]{{(b^{2})}^{3} \cdot 2 a}$

Step 1.4.4

Add parentheses.

$9 b^{2} \sqrt[3]{2 a} + 3 \sqrt[3]{{(b^{2})}^{3} \cdot (2 a)}$

Step 1.5

Pull terms out from under the radical.

$9 b^{2} \sqrt[3]{2 a} + 3 b^{2} \sqrt[3]{2 a}$

Step 2

Add $9 b^{2} \sqrt[3]{2 a}$ and $3 b^{2} \sqrt[3]{2 a}$ .

$12 b^{2} \sqrt[3]{2 a}$