Algebra Examples

$7 x^{3} y^{2} \sqrt{9 x^{7} y^{7}}$

Step 1

Rewrite $9 x^{7} y^{7}$ as ${(3 x^{3} y^{3})}^{2} (x y)$ .

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Step 1.1

Rewrite $9$ as $3^{2}$ .

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

Step 1.2

Factor out $x^{6}$ .

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

Step 1.3

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

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

Step 1.4

Factor out $y^{6}$ .

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

Step 1.5

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

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

Step 1.6

Move $x$ .

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

Step 1.7

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

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

Step 1.8

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Move $x^{3}$ .

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

Step 3.2

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

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

Step 3.3

Add $3$ and $3$ .

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

Step 4

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

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Step 4.1

Move $y^{3}$ .

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

Step 4.2

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

$7 x^{6} y^{3 + 2} (3 \sqrt{x y})$

Step 4.3

Add $3$ and $2$ .

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

Step 5

Multiply $3$ by $7$ .

$21 x^{6} y^{5} \sqrt{x y}$