Simplify the Radical Expression cube root of -6x^5* cube root of 18x^4

$\sqrt[3]{- 6 x^{5}} \cdot \sqrt[3]{18 x^{4}}$

Rewrite $- 6 x^{5}$ as ${(- x)}^{3} \cdot (6 x^{2})$ .

Rewrite $- 6$ as $- 1 (6)$ .

$\sqrt[3]{- 1 (6) x^{5}} \cdot \sqrt[3]{18 x^{4}}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$\sqrt[3]{{(- 1)}^{3} \cdot 6 x^{5}} \cdot \sqrt[3]{18 x^{4}}$

Factor out $x^{3}$ .

$\sqrt[3]{{(- 1)}^{3} \cdot 6 (x^{3} x^{2})} \cdot \sqrt[3]{18 x^{4}}$

Move $6$ .

$\sqrt[3]{{(- 1)}^{3} x^{3} \cdot 6 x^{2}} \cdot \sqrt[3]{18 x^{4}}$

Rewrite ${(- 1)}^{3} x^{3}$ as ${(- x)}^{3}$ .

$\sqrt[3]{{(- x)}^{3} \cdot 6 x^{2}} \cdot \sqrt[3]{18 x^{4}}$

Add parentheses.

$\sqrt[3]{{(- x)}^{3} \cdot (6 x^{2})} \cdot \sqrt[3]{18 x^{4}}$

Pull terms out from under the radical.

$- x \sqrt[3]{6 x^{2}} \cdot \sqrt[3]{18 x^{4}}$

Rewrite $18 x^{4}$ as $x^{3} \cdot (18 x)$ .

Factor out $x^{3}$ .

$- x \sqrt[3]{6 x^{2}} \cdot \sqrt[3]{18 (x^{3} x)}$

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

$- x \sqrt[3]{6 x^{2}} \cdot \sqrt[3]{x^{3} \cdot 18 x}$

Add parentheses.

$- x \sqrt[3]{6 x^{2}} \cdot \sqrt[3]{x^{3} \cdot (18 x)}$

Pull terms out from under the radical.

$- x \sqrt[3]{6 x^{2}} \cdot (x \sqrt[3]{18 x})$

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

Move $x$ .

$- (x \cdot x) \sqrt[3]{6 x^{2}} \cdot \sqrt[3]{18 x}$

Multiply $x$ by $x$ .

$- x^{2} \sqrt[3]{6 x^{2}} \cdot \sqrt[3]{18 x}$

Multiply $- x^{2} \sqrt[3]{6 x^{2}} \sqrt[3]{18 x}$ .

Combine using the product rule for radicals.

$- x^{2} \sqrt[3]{18 x (6 x^{2})}$

Multiply $6$ by $18$ .

$- x^{2} \sqrt[3]{108 x \cdot x^{2}}$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$- x^{2} \sqrt[3]{108 (x^{2} x)}$

Multiply $x^{2}$ by $x$ .

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

$- x^{2} \sqrt[3]{108 (x^{2} x^{1})}$

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

$- x^{2} \sqrt[3]{108 x^{2 + 1}}$

Add $2$ and $1$ .

$- x^{2} \sqrt[3]{108 x^{3}}$

Rewrite $108 x^{3}$ as ${(3 x)}^{3} \cdot 4$ .

Factor $27$ out of $108$ .

$- x^{2} \sqrt[3]{27 (4) x^{3}}$

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

$- x^{2} \sqrt[3]{3^{3} \cdot 4 x^{3}}$

Move $4$ .

$- x^{2} \sqrt[3]{3^{3} x^{3} \cdot 4}$

Rewrite $3^{3} x^{3}$ as ${(3 x)}^{3}$ .

$- x^{2} \sqrt[3]{{(3 x)}^{3} \cdot 4}$

Pull terms out from under the radical.

$- x^{2} (3 x \sqrt[3]{4})$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$- (x \cdot x^{2}) (3 \sqrt[3]{4})$

Multiply $x$ by $x^{2}$ .

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

$- (x^{1} x^{2}) (3 \sqrt[3]{4})$

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

$- x^{1 + 2} (3 \sqrt[3]{4})$

Add $1$ and $2$ .

$- x^{3} (3 \sqrt[3]{4})$

Multiply $3$ by $- 1$ .

$- 3 x^{3} \sqrt[3]{4}$

Simplify the Radical Expression cube root of -6x^5* cube root of 18x^4

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