Algebra Examples

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

Step 1

Rewrite $27 x^{3} y$ as ${(3 x)}^{3} y$ .

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Pull terms out from under the radical.

$3 x \sqrt[3]{y} (x \sqrt[3]{y})$

Step 4

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

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Step 4.1

Move $x$ .

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

Step 4.2

Multiply $x$ by $x$ .

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

Step 5

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

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Step 5.1

Raise $\sqrt[3]{y}$ to the power of $1$ .

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

Step 5.2

Raise $\sqrt[3]{y}$ to the power of $1$ .

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

Step 5.3

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

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

Step 5.4

Add $1$ and $1$ .

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

Step 6

Rewrite ${\sqrt[3]{y}}^{2}$ as $\sqrt[3]{y^{2}}$ .

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