Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Factor out $y^{6}$ .

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

Step 1.3

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

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

Step 1.4

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 4.1

Move $x$ .

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

Step 4.2

Multiply $x$ by $x^{2}$ .

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.3

Add $1$ and $2$ .

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

Step 5

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

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Step 5.1

Move $y^{3}$ .

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

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

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

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

Step 5.3

Add $3$ and $1$ .

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