Evaluate 3b^2( cube root of 54a)+3( cube root of 2ab^6)

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

Step 1

Simplify each term.

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

Factor $27$ out of $54$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $3$ by $3$ .

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

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

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

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

Move $a$ .

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

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

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

Add parentheses.

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

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

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