Simplify the Radical Expression cube root of 3x^2* cube root of x^2* cube root of 9x^3

$\sqrt[3]{3 x^{2}} \cdot \sqrt[3]{x^{2}} \cdot \sqrt[3]{9 x^{3}}$

Step 1

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

Combine using the product rule for radicals.

$\sqrt[3]{3 x^{2} x^{2}} \cdot \sqrt[3]{9 x^{3}}$

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

Move $x^{2}$ .

$\sqrt[3]{3 (x^{2} x^{2})} \cdot \sqrt[3]{9 x^{3}}$

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

$\sqrt[3]{3 x^{2 + 2}} \cdot \sqrt[3]{9 x^{3}}$

Add $2$ and $2$ .

$\sqrt[3]{3 x^{4}} \cdot \sqrt[3]{9 x^{3}}$

Step 2

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

Factor out $x^{3}$ .

$\sqrt[3]{3 (x^{3} x)} \cdot \sqrt[3]{9 x^{3}}$

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

$\sqrt[3]{x^{3} \cdot 3 x} \cdot \sqrt[3]{9 x^{3}}$

Add parentheses.

$\sqrt[3]{x^{3} \cdot (3 x)} \cdot \sqrt[3]{9 x^{3}}$

Step 3

Pull terms out from under the radical.

$x \sqrt[3]{3 x} \cdot \sqrt[3]{9 x^{3}}$

Step 4

Reorder $9$ and $x^{3}$ .

$x \sqrt[3]{3 x} \cdot \sqrt[3]{x^{3} \cdot 9}$

Step 5

Pull terms out from under the radical.

$x \sqrt[3]{3 x} \cdot (x \sqrt[3]{9})$

Step 6

Rewrite using the commutative property of multiplication.

$\sqrt[3]{9} x \sqrt[3]{3 x} x$

Step 7

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

Move $x$ .

$\sqrt[3]{9} (x \cdot x) \sqrt[3]{3 x}$

Multiply $x$ by $x$ .

$\sqrt[3]{9} x^{2} \sqrt[3]{3 x}$

Step 8

Multiply $\sqrt[3]{9} x^{2} \sqrt[3]{3 x}$ .

Combine using the product rule for radicals.

$x^{2} \sqrt[3]{9 (3 x)}$

Multiply $9$ by $3$ .

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

Step 9

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

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

Step 10

Pull terms out from under the radical.

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

Step 11

Rewrite using the commutative property of multiplication.

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

Simplify the Radical Expression cube root of 3x^2* cube root of x^2* cube root of 9x^3

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