Algebra Examples

$\frac{30 x^{7} y^{- 3}}{5 x^{4} y^{2}} \cdot \frac{x^{- 5}}{y^{- 8}}$

Step 1

Combine.

$\frac{30 x^{7} y^{- 3} x^{- 5}}{5 x^{4} y^{2} y^{- 8}}$

Step 2

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

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Step 2.1

Move $x^{- 5}$ .

$\frac{30 (x^{- 5} x^{7}) y^{- 3}}{5 x^{4} y^{2} y^{- 8}}$

Step 2.2

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

$\frac{30 x^{- 5 + 7} y^{- 3}}{5 x^{4} y^{2} y^{- 8}}$

Step 2.3

Add $- 5$ and $7$ .

$\frac{30 x^{2} y^{- 3}}{5 x^{4} y^{2} y^{- 8}}$

Step 3

Multiply $y^{2}$ by $y^{- 8}$ by adding the exponents.

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Step 3.1

Move $y^{- 8}$ .

$\frac{30 x^{2} y^{- 3}}{5 x^{4} (y^{- 8} y^{2})}$

Step 3.2

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

$\frac{30 x^{2} y^{- 3}}{5 x^{4} y^{- 8 + 2}}$

Step 3.3

Add $- 8$ and $2$ .

$\frac{30 x^{2} y^{- 3}}{5 x^{4} y^{- 6}}$

Step 4

Move $y^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{30 x^{2} y^{- 3} y^{6}}{5 x^{4}}$

Step 5

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

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Step 5.1

Move $y^{6}$ .

$\frac{30 x^{2} (y^{6} y^{- 3})}{5 x^{4}}$

Step 5.2

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

$\frac{30 x^{2} y^{6 - 3}}{5 x^{4}}$

Step 5.3

Subtract $3$ from $6$ .

$\frac{30 x^{2} y^{3}}{5 x^{4}}$

Step 6

Cancel the common factor of $30$ and $5$ .

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Step 6.1

Factor $5$ out of $30 x^{2} y^{3}$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $5 x^{4}$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

Cancel the common factor of $x^{2}$ and $x^{4}$ .

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Step 7.1

Factor $x^{2}$ out of $6 x^{2} y^{3}$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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