Basic Math Examples

$\frac{\frac{15 y^{- 7}}{22 y^{5}}}{\frac{9 y^{- 5}}{4 y^{- 2}}}$

Step 1

Cancel the common factor of $y^{- 7}$ and $y^{5}$ .

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Step 1.1

Factor $y^{- 7}$ out of $15 y^{- 7}$ .

$\frac{\frac{y^{- 7} \cdot 15}{22 y^{5}}}{\frac{9 y^{- 5}}{4 y^{- 2}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $y^{- 7}$ out of $22 y^{5}$ .

$\frac{\frac{y^{- 7} \cdot 15}{y^{- 7} (22 y^{12})}}{\frac{9 y^{- 5}}{4 y^{- 2}}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{y^{- 7} \cdot 15}{y^{- 7} (22 y^{12})}}{\frac{9 y^{- 5}}{4 y^{- 2}}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{15}{22 y^{12}}}{\frac{9 y^{- 5}}{4 y^{- 2}}}$

Step 2

Cancel the common factor of $y^{- 5}$ and $y^{- 2}$ .

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Step 2.1

Factor $y^{- 5}$ out of $9 y^{- 5}$ .

$\frac{\frac{15}{22 y^{12}}}{\frac{y^{- 5} \cdot 9}{4 y^{- 2}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $y^{- 5}$ out of $4 y^{- 2}$ .

$\frac{\frac{15}{22 y^{12}}}{\frac{y^{- 5} \cdot 9}{y^{- 5} (4 y^{3})}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{15}{22 y^{12}}}{\frac{y^{- 5} \cdot 9}{y^{- 5} (4 y^{3})}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{15}{22 y^{12}}}{\frac{9}{4 y^{3}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{22 y^{12}} \cdot \frac{4 y^{3}}{9}$

Step 4

Simplify terms.

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Step 4.1

Combine.

$\frac{15 (4 y^{3})}{22 y^{12} \cdot 9}$

Step 4.2

Cancel the common factor of $15$ and $9$ .

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Step 4.2.1

Factor $3$ out of $15 (4 y^{3})$ .

$\frac{3 (5 (4 y^{3}))}{22 y^{12} \cdot 9}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $3$ out of $22 y^{12} \cdot 9$ .

$\frac{3 (5 (4 y^{3}))}{3 (22 y^{12} \cdot 3)}$

Step 4.2.2.2

Cancel the common factor.

$\frac{3 (5 (4 y^{3}))}{3 (22 y^{12} \cdot 3)}$

Step 4.2.2.3

Rewrite the expression.

$\frac{5 (4 y^{3})}{22 y^{12} \cdot 3}$

Step 4.3

Cancel the common factor of $4$ and $22$ .

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Step 4.3.1

Factor $2$ out of $5 (4 y^{3})$ .

$\frac{2 (5 (2 y^{3}))}{22 y^{12} \cdot 3}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $22 y^{12} \cdot 3$ .

$\frac{2 (5 (2 y^{3}))}{2 (11 y^{12} \cdot 3)}$

Step 4.3.2.2

Cancel the common factor.

$\frac{2 (5 (2 y^{3}))}{2 (11 y^{12} \cdot 3)}$

Step 4.3.2.3

Rewrite the expression.

$\frac{5 (2 y^{3})}{11 y^{12} \cdot 3}$

Step 4.4

Cancel the common factor of $y^{3}$ and $y^{12}$ .

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Step 4.4.1

Factor $y^{3}$ out of $5 (2 y^{3})$ .

$\frac{y^{3} (5 \cdot (2))}{11 y^{12} \cdot 3}$

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $y^{3}$ out of $11 y^{12} \cdot 3$ .

$\frac{y^{3} (5 \cdot (2))}{y^{3} (11 y^{9} \cdot 3)}$

Step 4.4.2.2

Cancel the common factor.

$\frac{y^{3} (5 \cdot (2))}{y^{3} (11 y^{9} \cdot 3)}$

Step 4.4.2.3

Rewrite the expression.

$\frac{5 \cdot (2)}{11 y^{9} \cdot 3}$

Step 5

Multiply $5$ by $2$ .

$\frac{10}{11 y^{9} \cdot 3}$

Step 6

Multiply $3$ by $11$ .

$\frac{10}{33 y^{9}}$