Algebra Examples

$\sqrt{x^{7} y^{7}} \cdot 3 \sqrt{5 x^{3} y^{2}}$

Step 1

Rewrite using the commutative property of multiplication.

$3 \sqrt{x^{7} y^{7}} \sqrt{5 x^{3} y^{2}}$

Step 2

Rewrite $x^{7} y^{7}$ as ${(x^{3} y^{3})}^{2} (x y)$ .

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Step 2.1

Factor out $x^{6}$ .

$3 \sqrt{x^{6} x y^{7}} \sqrt{5 x^{3} y^{2}}$

Step 2.2

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

$3 \sqrt{{(x^{3})}^{2} x y^{7}} \sqrt{5 x^{3} y^{2}}$

Step 2.3

Factor out $y^{6}$ .

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

Step 2.4

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

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

Step 2.5

Move $x$ .

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

Step 2.6

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

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

Step 2.7

Add parentheses.

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

Step 3

Pull terms out from under the radical.

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

Step 4

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

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Step 4.1

Factor out $x^{2}$ .

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

Step 4.2

Move $x$ .

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

Step 4.3

Move $5$ .

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

Step 4.4

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

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

Step 4.5

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 6.1

Move $x$ .

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

Step 6.2

Multiply $x$ by $x^{3}$ .

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Step 6.2.1

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

$3 (x^{1} x^{3}) y^{3} \sqrt{x y} (y \sqrt{5 x})$

Step 6.2.2

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

$3 x^{1 + 3} y^{3} \sqrt{x y} (y \sqrt{5 x})$

Step 6.3

Add $1$ and $3$ .

$3 x^{4} y^{3} \sqrt{x y} (y \sqrt{5 x})$

Step 7

Multiply $y^{3}$ by $y$ by adding the exponents.

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Step 7.1

Move $y$ .

$3 x^{4} (y \cdot y^{3}) \sqrt{x y} \sqrt{5 x}$

Step 7.2

Multiply $y$ by $y^{3}$ .

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Step 7.2.1

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

$3 x^{4} (y^{1} y^{3}) \sqrt{x y} \sqrt{5 x}$

Step 7.2.2

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

$3 x^{4} y^{1 + 3} \sqrt{x y} \sqrt{5 x}$

Step 7.3

Add $1$ and $3$ .

$3 x^{4} y^{4} \sqrt{x y} \sqrt{5 x}$

Step 8

Multiply $3 x^{4} y^{4} \sqrt{x y} \sqrt{5 x}$ .

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Step 8.1

Combine using the product rule for radicals.

$3 x^{4} y^{4} \sqrt{5 x (x y)}$

Step 8.2

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

$3 x^{4} y^{4} \sqrt{5 (x^{1} x) y}$

Step 8.3

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

$3 x^{4} y^{4} \sqrt{5 (x^{1} x^{1}) y}$

Step 8.4

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

$3 x^{4} y^{4} \sqrt{5 x^{1 + 1} y}$

Step 8.5

Add $1$ and $1$ .

$3 x^{4} y^{4} \sqrt{5 x^{2} y}$

Step 9

Rewrite $5 x^{2} y$ as $x^{2} \cdot (5 y)$ .

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Step 9.1

Reorder $5$ and $x^{2}$ .

$3 x^{4} y^{4} \sqrt{x^{2} \cdot 5 y}$

Step 9.2

Add parentheses.

$3 x^{4} y^{4} \sqrt{x^{2} \cdot (5 y)}$

Step 10

Pull terms out from under the radical.

$3 x^{4} y^{4} (x \sqrt{5 y})$

Step 11

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 11.1

Move $x$ .

$3 (x \cdot x^{4}) y^{4} \sqrt{5 y}$

Step 11.2

Multiply $x$ by $x^{4}$ .

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Step 11.2.1

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

$3 (x^{1} x^{4}) y^{4} \sqrt{5 y}$

Step 11.2.2

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

$3 x^{1 + 4} y^{4} \sqrt{5 y}$

Step 11.3

Add $1$ and $4$ .

$3 x^{5} y^{4} \sqrt{5 y}$