Algebra Examples

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

Step 1

Apply the product rule to $3 \sqrt{2 x y}$ .

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

Step 2

Raise $3$ to the power of $3$ .

$27 {\sqrt{2 x y}}^{3}$

Step 3

Rewrite ${\sqrt{2 x y}}^{3}$ as $\sqrt{{(2 x y)}^{3}}$ .

$27 \sqrt{{(2 x y)}^{3}}$

Step 4

Apply the product rule to $2 x y$ .

$27 \sqrt{{(2 x)}^{3} y^{3}}$

Step 5

Apply the product rule to $2 x$ .

$27 \sqrt{2^{3} x^{3} y^{3}}$

Step 6

Raise $2$ to the power of $3$ .

$27 \sqrt{8 x^{3} y^{3}}$

Step 7

Rewrite $8 x^{3} y^{3}$ as ${(2 x y)}^{2} \cdot (2 x y)$ .

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Step 7.1

Factor $4$ out of $8$ .

$27 \sqrt{4 (2) x^{3} y^{3}}$

Step 7.2

Rewrite $4$ as $2^{2}$ .

$27 \sqrt{2^{2} \cdot 2 x^{3} y^{3}}$

Step 7.3

Factor out $x^{2}$ .

$27 \sqrt{2^{2} \cdot 2 (x^{2} x) y^{3}}$

Step 7.4

Factor out $y^{2}$ .

$27 \sqrt{2^{2} \cdot 2 (x^{2} x) (y^{2} y)}$

Step 7.5

Move $x$ .

$27 \sqrt{2^{2} \cdot 2 (x^{2}) y^{2} x y}$

Step 7.6

Move $2$ .

$27 \sqrt{(2^{2} (x^{2})) y^{2} \cdot 2 x y}$

Step 7.7

Rewrite $(2^{2} (x^{2})) y^{2}$ as ${(2 x y)}^{2}$ .

$27 \sqrt{{(2 x y)}^{2} \cdot 2 x y}$

Step 7.8

Add parentheses.

$27 \sqrt{{(2 x y)}^{2} \cdot 2 (x y)}$

Step 7.9

Add parentheses.

$27 \sqrt{{(2 x y)}^{2} \cdot (2 x y)}$

Step 8

Pull terms out from under the radical.

$27 (2 x y \sqrt{2 x y})$

Step 9

Multiply $2$ by $27$ .

$54 x y \sqrt{2 x y}$