Algebra Examples

$\frac{x^{- 6} y^{9}}{x y^{- 3}} \cdot \frac{x^{- 3}}{y^{12}}$

Step 1

Combine.

$\frac{x^{- 6} y^{9} x^{- 3}}{x y^{- 3} y^{12}}$

Step 2

Multiply $x^{- 6}$ by $x^{- 3}$ by adding the exponents.

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Step 2.1

Move $x^{- 3}$ .

$\frac{x^{- 3} x^{- 6} y^{9}}{x y^{- 3} y^{12}}$

Step 2.2

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

$\frac{x^{- 3 - 6} y^{9}}{x y^{- 3} y^{12}}$

Step 2.3

Subtract $6$ from $- 3$ .

$\frac{x^{- 9} y^{9}}{x y^{- 3} y^{12}}$

Step 3

Multiply $y^{- 3}$ by $y^{12}$ by adding the exponents.

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Step 3.1

Move $y^{12}$ .

$\frac{x^{- 9} y^{9}}{x (y^{12} y^{- 3})}$

Step 3.2

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

$\frac{x^{- 9} y^{9}}{x y^{12 - 3}}$

Step 3.3

Subtract $3$ from $12$ .

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

Step 4

Move $x^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{9}}{x y^{9} x^{9}}$

Step 5

Multiply $x$ by $x^{9}$ by adding the exponents.

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Step 5.1

Move $x^{9}$ .

$\frac{y^{9}}{x^{9} x y^{9}}$

Step 5.2

Multiply $x^{9}$ by $x$ .

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Step 5.2.1

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

$\frac{y^{9}}{x^{9} x^{1} y^{9}}$

Step 5.2.2

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

$\frac{y^{9}}{x^{9 + 1} y^{9}}$

Step 5.3

Add $9$ and $1$ .

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

Step 6

Cancel the common factor of $y^{9}$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{1}{x^{10}}$