Simplify (5 cube root of 3x^3)(3 cube root of 18x^3)

$(5 \sqrt[3]{3 x^{3}}) (3 \sqrt[3]{18 x^{3}})$

Step 1

Reorder $3$ and $x^{3}$ .

$5 \sqrt[3]{x^{3} \cdot 3} (3 \sqrt[3]{18 x^{3}})$

Step 2

Pull terms out from under the radical.

$5 (x \sqrt[3]{3}) (3 \sqrt[3]{18 x^{3}})$

Step 3

Reorder $18$ and $x^{3}$ .

$5 x \sqrt[3]{3} (3 \sqrt[3]{x^{3} \cdot 18})$

Step 4

Pull terms out from under the radical.

$5 x \sqrt[3]{3} (3 (x \sqrt[3]{18}))$

Step 5

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$5 (x \cdot x) \sqrt[3]{3} (3 (\sqrt[3]{18}))$

Multiply $x$ by $x$ .

$5 x^{2} \sqrt[3]{3} (3 (\sqrt[3]{18}))$

$5 x^{2} \sqrt[3]{3} (3 (\sqrt[3]{18}))$

Step 6

Multiply $5 x^{2} \sqrt[3]{3} (3 \sqrt[3]{18})$ .

Multiply $3$ by $5$ .

$15 x^{2} \sqrt[3]{3} \sqrt[3]{18}$

Combine using the product rule for radicals.

$15 x^{2} \sqrt[3]{18 \cdot 3}$

Multiply $18$ by $3$ .

$15 x^{2} \sqrt[3]{54}$

$15 x^{2} \sqrt[3]{54}$

Step 7

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

Factor $27$ out of $54$ .

$15 x^{2} \sqrt[3]{27 (2)}$

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

$15 x^{2} \sqrt[3]{3^{3} \cdot 2}$

$15 x^{2} \sqrt[3]{3^{3} \cdot 2}$

Step 8

Pull terms out from under the radical.

$15 x^{2} (3 \sqrt[3]{2})$

Step 9

Multiply $3$ by $15$ .

$45 x^{2} \sqrt[3]{2}$

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