Algebra Examples

$\frac{9 x^{- 4} y^{7}}{18 x^{6} y^{- 2}} \cdot \frac{3 x^{8}}{y^{3}}$

Step 1

Combine.

$\frac{9 x^{- 4} y^{7} (3 x^{8})}{18 x^{6} y^{- 2} y^{3}}$

Step 2

Multiply $x^{- 4}$ by $x^{8}$ by adding the exponents.

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Step 2.1

Move $x^{8}$ .

$\frac{9 (x^{8} x^{- 4}) y^{7} \cdot 3}{18 x^{6} y^{- 2} y^{3}}$

Step 2.2

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

$\frac{9 x^{8 - 4} y^{7} \cdot 3}{18 x^{6} y^{- 2} y^{3}}$

Step 2.3

Subtract $4$ from $8$ .

$\frac{9 x^{4} y^{7} \cdot 3}{18 x^{6} y^{- 2} y^{3}}$

Step 3

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

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Step 3.1

Move $y^{3}$ .

$\frac{9 x^{4} y^{7} \cdot 3}{18 x^{6} (y^{3} y^{- 2})}$

Step 3.2

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

$\frac{9 x^{4} y^{7} \cdot 3}{18 x^{6} y^{3 - 2}}$

Step 3.3

Subtract $2$ from $3$ .

$\frac{9 x^{4} y^{7} \cdot 3}{18 x^{6} y^{1}}$

Step 4

Simplify $18 x^{6} y^{1}$ .

$\frac{9 x^{4} y^{7} \cdot 3}{18 x^{6} y}$

Step 5

Cancel the common factor of $9$ and $18$ .

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Step 5.1

Factor $9$ out of $9 x^{4} y^{7} \cdot 3$ .

$\frac{9 (x^{4} y^{7} \cdot 3)}{18 x^{6} y}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $9$ out of $18 x^{6} y$ .

$\frac{9 (x^{4} y^{7} \cdot 3)}{9 (2 x^{6} y)}$

Step 5.2.2

Cancel the common factor.

$\frac{9 (x^{4} y^{7} \cdot 3)}{9 (2 x^{6} y)}$

Step 5.2.3

Rewrite the expression.

$\frac{x^{4} y^{7} \cdot 3}{2 x^{6} y}$

Step 6

Cancel the common factor of $x^{4}$ and $x^{6}$ .

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Step 6.1

Factor $x^{4}$ out of $x^{4} y^{7} \cdot 3$ .

$\frac{x^{4} (y^{7} \cdot 3)}{2 x^{6} y}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $x^{4}$ out of $2 x^{6} y$ .

$\frac{x^{4} (y^{7} \cdot 3)}{x^{4} (2 x^{2} y)}$

Step 6.2.2

Cancel the common factor.

$\frac{x^{4} (y^{7} \cdot 3)}{x^{4} (2 x^{2} y)}$

Step 6.2.3

Rewrite the expression.

$\frac{y^{7} \cdot 3}{2 x^{2} y}$

Step 7

Cancel the common factor of $y^{7}$ and $y$ .

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Step 7.1

Factor $y$ out of $y^{7} \cdot 3$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$\frac{y^{6} \cdot 3}{2 x^{2}}$

Step 8

Move $3$ to the left of $y^{6}$ .

$\frac{3 y^{6}}{2 x^{2}}$