Algebra Examples

$5 \sqrt{2 x y^{6}} \cdot 2 \sqrt{2 x^{3} y}$

Step 1

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

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Step 1.1

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

$5 \sqrt{2 x {(y^{3})}^{2}} \cdot (2 \sqrt{2 x^{3} y})$

Step 1.2

Move $x$ .

$5 \sqrt{2 {(y^{3})}^{2} x} \cdot (2 \sqrt{2 x^{3} y})$

Step 1.3

Reorder $2$ and ${(y^{3})}^{2}$ .

$5 \sqrt{{(y^{3})}^{2} \cdot 2 x} \cdot (2 \sqrt{2 x^{3} y})$

Step 1.4

Add parentheses.

$5 \sqrt{{(y^{3})}^{2} \cdot (2 x)} \cdot (2 \sqrt{2 x^{3} y})$

Step 2

Pull terms out from under the radical.

$5 (y^{3} \sqrt{2 x}) \cdot (2 \sqrt{2 x^{3} y})$

Step 3

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

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Step 3.1

Factor out $x^{2}$ .

$5 y^{3} \sqrt{2 x} \cdot (2 \sqrt{2 (x^{2} x) y})$

Step 3.2

Reorder $2$ and $x^{2}$ .

$5 y^{3} \sqrt{2 x} \cdot (2 \sqrt{x^{2} \cdot 2 x y})$

Step 3.3

Add parentheses.

$5 y^{3} \sqrt{2 x} \cdot (2 \sqrt{x^{2} \cdot 2 (x y)})$

Step 3.4

Add parentheses.

$5 y^{3} \sqrt{2 x} \cdot (2 \sqrt{x^{2} \cdot (2 x y)})$

Step 4

Pull terms out from under the radical.

$5 y^{3} \sqrt{2 x} \cdot (2 (x \sqrt{2 x y}))$

Step 5

Multiply $5 y^{3} \sqrt{2 x} (2 x \sqrt{2 x y})$ .

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Step 5.1

Multiply $2$ by $5$ .

$10 y^{3} \sqrt{2 x} (x \sqrt{2 x y})$

Step 5.2

Combine using the product rule for radicals.

$10 y^{3} (x \sqrt{2 x (2 x y)})$

Step 5.3

Multiply $2$ by $2$ .

$10 y^{3} (x \sqrt{4 x (x y)})$

Step 5.4

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

$10 y^{3} (x \sqrt{4 (x^{1} x) y})$

Step 5.5

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

$10 y^{3} (x \sqrt{4 (x^{1} x^{1}) y})$

Step 5.6

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

$10 y^{3} (x \sqrt{4 x^{1 + 1} y})$

Step 5.7

Add $1$ and $1$ .

$10 y^{3} (x \sqrt{4 x^{2} y})$

Step 6

Rewrite $4 x^{2} y$ as ${(2 x)}^{2} y$ .

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Step 6.1

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

$10 y^{3} (x \sqrt{2^{2} x^{2} y})$

Step 6.2

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

$10 y^{3} (x \sqrt{{(2 x)}^{2} y})$

Step 7

Pull terms out from under the radical.

$10 y^{3} (x (2 x \sqrt{y}))$

Step 8

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

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Step 8.1

Move $x$ .

$10 y^{3} (x \cdot x (2 \sqrt{y}))$

Step 8.2

Multiply $x$ by $x$ .

$10 y^{3} (x^{2} (2 \sqrt{y}))$

Step 9

Rewrite using the commutative property of multiplication.

$10 y^{3} (2 x^{2} \sqrt{y})$

Step 10

Multiply $2$ by $10$ .

$20 y^{3} (x^{2} \sqrt{y})$

Step 11

Reorder factors in $20 y^{3} (x^{2} \sqrt{y})$ .

$20 y^{3} x^{2} \sqrt{y}$