Algebra Examples

$\frac{15 x^{2} y \cdot - 6 x^{7} y}{{(3 x y)}^{2}}$

Step 1

Multiply $x^{2}$ by $x^{7}$ by adding the exponents.

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Step 1.1

Move $x^{7}$ .

$\frac{15 (x^{7} x^{2}) y \cdot (- 6 y)}{{(3 x y)}^{2}}$

Step 1.2

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

$\frac{15 x^{7 + 2} y \cdot (- 6 y)}{{(3 x y)}^{2}}$

Step 1.3

Add $7$ and $2$ .

$\frac{15 x^{9} y \cdot (- 6 y)}{{(3 x y)}^{2}}$

Step 2

Multiply $y$ by $y$ by adding the exponents.

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Step 2.1

Move $y$ .

$\frac{15 x^{9} (y \cdot y) \cdot - 6}{{(3 x y)}^{2}}$

Step 2.2

Multiply $y$ by $y$ .

$\frac{15 x^{9} y^{2} \cdot - 6}{{(3 x y)}^{2}}$

Step 3

Multiply $- 6$ by $15$ .

$\frac{- 90 x^{9} y^{2}}{{(3 x y)}^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $3 x y$ .

$\frac{- 90 x^{9} y^{2}}{{(3 x)}^{2} y^{2}}$

Step 4.2

Apply the product rule to $3 x$ .

$\frac{- 90 x^{9} y^{2}}{3^{2} x^{2} y^{2}}$

Step 4.3

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

$\frac{- 90 x^{9} y^{2}}{9 x^{2} y^{2}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $- 90$ and $9$ .

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Step 5.1.1

Factor $9$ out of $- 90 x^{9} y^{2}$ .

$\frac{9 (- 10 x^{9} y^{2})}{9 x^{2} y^{2}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $9$ out of $9 x^{2} y^{2}$ .

$\frac{9 (- 10 x^{9} y^{2})}{9 (x^{2} y^{2})}$

Step 5.1.2.2

Cancel the common factor.

$\frac{9 (- 10 x^{9} y^{2})}{9 (x^{2} y^{2})}$

Step 5.1.2.3

Rewrite the expression.

$\frac{- 10 x^{9} y^{2}}{x^{2} y^{2}}$

Step 5.2

Cancel the common factor of $x^{9}$ and $x^{2}$ .

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Step 5.2.1

Factor $x^{2}$ out of $- 10 x^{9} y^{2}$ .

$\frac{x^{2} (- 10 x^{7} y^{2})}{x^{2} y^{2}}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $x^{2}$ out of $x^{2} y^{2}$ .

$\frac{x^{2} (- 10 x^{7} y^{2})}{x^{2} (y^{2})}$

Step 5.2.2.2

Cancel the common factor.

$\frac{x^{2} (- 10 x^{7} y^{2})}{x^{2} y^{2}}$

Step 5.2.2.3

Rewrite the expression.

$\frac{- 10 x^{7} y^{2}}{y^{2}}$

Step 5.3

Cancel the common factor of $y^{2}$ .

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Step 5.3.1

Cancel the common factor.

$\frac{- 10 x^{7} y^{2}}{y^{2}}$

Step 5.3.2

Divide $- 10 x^{7}$ by $1$ .

$- 10 x^{7}$