Basic Math Examples

$\frac{16 a^{3} y}{- 4 a y^{3}} \cdot (- \frac{2 a y}{- a^{- 1}})$

Step 1

Rewrite using the commutative property of multiplication.

$- \frac{16 a^{3} y}{- 4 a y^{3}} \cdot \frac{2 a y}{- a^{- 1}}$

Step 2

Cancel the common factor of $a^{- 1}$ .

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Step 2.1

Move the leading negative in $- \frac{16 a^{3} y}{- 4 a y^{3}}$ into the numerator.

$\frac{- 16 a^{3} y}{- 4 a y^{3}} \cdot \frac{2 a y}{- a^{- 1}}$

Step 2.2

Factor $a^{- 1}$ out of $- 16 a^{3} y$ .

$\frac{a^{- 1} (- 16 a^{4} y)}{- 4 a y^{3}} \cdot \frac{2 a y}{- a^{- 1}}$

Step 2.3

Factor $a^{- 1}$ out of $- a^{- 1}$ .

$\frac{a^{- 1} (- 16 a^{4} y)}{- 4 a y^{3}} \cdot \frac{2 a y}{a^{- 1} \cdot - 1}$

Step 2.4

Cancel the common factor.

$\frac{a^{- 1} (- 16 a^{4} y)}{- 4 a y^{3}} \cdot \frac{2 a y}{a^{- 1} \cdot - 1}$

Step 2.5

Rewrite the expression.

$\frac{- 16 a^{4} y}{- 4 a y^{3}} \cdot \frac{2 a y}{- 1}$

Step 3

Cancel the common factor of $2 a y$ .

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Step 3.1

Factor $2 a y$ out of $- 4 a y^{3}$ .

$\frac{- 16 a^{4} y}{2 a y (- 2 y^{2})} \cdot \frac{2 a y}{- 1}$

Step 3.2

Cancel the common factor.

$\frac{- 16 a^{4} y}{2 a y (- 2 y^{2})} \cdot \frac{2 a y}{- 1}$

Step 3.3

Rewrite the expression.

$\frac{- 16 a^{4} y}{- 2 y^{2}} \cdot \frac{1}{- 1}$

Step 4

Multiply $\frac{- 16 a^{4} y}{- 2 y^{2}}$ by $\frac{1}{- 1}$ .

$\frac{- 16 a^{4} y}{- 2 y^{2} \cdot - 1}$

Step 5

Multiply $- 1$ by $- 2$ .

$\frac{- 16 a^{4} y}{2 y^{2}}$

Step 6

Cancel the common factor of $- 16$ and $2$ .

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Step 6.1

Factor $2$ out of $- 16 a^{4} y$ .

$\frac{2 (- 8 a^{4} y)}{2 y^{2}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{2 (- 8 a^{4} y)}{2 (y^{2})}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (- 8 a^{4} y)}{2 y^{2}}$

Step 6.2.3

Rewrite the expression.

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

Step 7

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

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Step 7.1

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

$\frac{y (- 8 a^{4})}{y^{2}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{y (- 8 a^{4})}{y \cdot y}$

Step 7.2.2

Cancel the common factor.

$\frac{y (- 8 a^{4})}{y \cdot y}$

Step 7.2.3

Rewrite the expression.

$\frac{- 8 a^{4}}{y}$

Step 8

Move the negative in front of the fraction.

$- \frac{8 a^{4}}{y}$