Algebra Examples

$\frac{8 x^{4} y^{5} x^{- 6} y^{- 7}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 1

Multiply $x^{4}$ by $x^{- 6}$ by adding the exponents.

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Step 1.1

Move $x^{- 6}$ .

$\frac{8 (x^{- 6} x^{4}) y^{5} y^{- 7}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 1.2

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

$\frac{8 x^{- 6 + 4} y^{5} y^{- 7}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 1.3

Add $- 6$ and $4$ .

$\frac{8 x^{- 2} y^{5} y^{- 7}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 2

Multiply $y^{5}$ by $y^{- 7}$ by adding the exponents.

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Step 2.1

Move $y^{- 7}$ .

$\frac{8 x^{- 2} (y^{- 7} y^{5})}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 2.2

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

$\frac{8 x^{- 2} y^{- 7 + 5}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 2.3

Add $- 7$ and $5$ .

$\frac{8 x^{- 2} y^{- 2}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 3

Multiply $x^{2}$ by $x^{- 4}$ by adding the exponents.

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Step 3.1

Move $x^{- 4}$ .

$\frac{8 x^{- 2} y^{- 2}}{4 (x^{- 4} x^{2}) y^{3} y^{- 5}}$

Step 3.2

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

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 4 + 2} y^{3} y^{- 5}}$

Step 3.3

Add $- 4$ and $2$ .

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 2} y^{3} y^{- 5}}$

Step 4

Multiply $y^{3}$ by $y^{- 5}$ by adding the exponents.

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Step 4.1

Move $y^{- 5}$ .

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 2} (y^{- 5} y^{3})}$

Step 4.2

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

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 2} y^{- 5 + 3}}$

Step 4.3

Add $- 5$ and $3$ .

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 2} y^{- 2}}$

Step 5

Cancel the common factor of $8$ and $4$ .

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Step 5.1

Factor $4$ out of $8 x^{- 2} y^{- 2}$ .

$\frac{4 (2 x^{- 2} y^{- 2})}{4 x^{- 2} y^{- 2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{4 (2 x^{- 2} y^{- 2})}{4 (x^{- 2} y^{- 2})}$

Step 5.2.2

Cancel the common factor.

$\frac{4 (2 x^{- 2} y^{- 2})}{4 (x^{- 2} y^{- 2})}$

Step 5.2.3

Rewrite the expression.

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{2 y^{- 2}}{y^{- 2}}$

Step 7

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

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Step 7.1

Cancel the common factor.

$\frac{2 y^{- 2}}{y^{- 2}}$

Step 7.2

Divide $2$ by $1$ .

$2$