Algebra Examples

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

Step 1

Combine.

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

Step 2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1

Move $x$ .

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

Step 2.2

Multiply $x$ by $x$ .

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

Step 3

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

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Step 3.1

Move $y^{3}$ .

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

Step 3.2

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

$\frac{2 x^{2} y^{3 + 2} \cdot 5}{x^{5} y^{3} (- 30 y^{- 2})}$

Step 3.3

Add $3$ and $2$ .

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

Step 4

Multiply $y^{3}$ by $y^{- 2}$ by adding the exponents.

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Step 4.1

Move $y^{- 2}$ .

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

Step 4.2

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

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

Step 4.3

Add $- 2$ and $3$ .

$\frac{2 x^{2} y^{5} \cdot 5}{x^{5} y^{1} \cdot - 30}$

Step 5

Simplify $x^{5} y^{1} \cdot - 30$ .

$\frac{2 x^{2} y^{5} \cdot 5}{x^{5} y \cdot - 30}$

Step 6

Cancel the common factor of $2$ and $- 30$ .

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Step 6.1

Factor $2$ out of $2 x^{2} y^{5} \cdot 5$ .

$\frac{2 (x^{2} y^{5} \cdot 5)}{x^{5} y \cdot - 30}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $x^{5} y \cdot - 30$ .

$\frac{2 (x^{2} y^{5} \cdot 5)}{2 (x^{5} y \cdot - 15)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (x^{2} y^{5} \cdot 5)}{2 (x^{5} y \cdot - 15)}$

Step 6.2.3

Rewrite the expression.

$\frac{x^{2} y^{5} \cdot 5}{x^{5} y \cdot - 15}$

Step 7

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

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Step 7.1

Factor $x^{2}$ out of $x^{2} y^{5} \cdot 5$ .

$\frac{x^{2} (y^{5} \cdot 5)}{x^{5} y \cdot - 15}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $x^{2}$ out of $x^{5} y \cdot - 15$ .

$\frac{x^{2} (y^{5} \cdot 5)}{x^{2} (x^{3} y \cdot - 15)}$

Step 7.2.2

Cancel the common factor.

$\frac{x^{2} (y^{5} \cdot 5)}{x^{2} (x^{3} y \cdot - 15)}$

Step 7.2.3

Rewrite the expression.

$\frac{y^{5} \cdot 5}{x^{3} y \cdot - 15}$

Step 8

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

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Step 8.1

Factor $y$ out of $y^{5} \cdot 5$ .

$\frac{y (y^{4} \cdot 5)}{x^{3} y \cdot - 15}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $y$ out of $x^{3} y \cdot - 15$ .

$\frac{y (y^{4} \cdot 5)}{y (x^{3} \cdot - 15)}$

Step 8.2.2

Cancel the common factor.

$\frac{y (y^{4} \cdot 5)}{y (x^{3} \cdot - 15)}$

Step 8.2.3

Rewrite the expression.

$\frac{y^{4} \cdot 5}{x^{3} \cdot - 15}$

Step 9

Cancel the common factor of $5$ and $- 15$ .

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Step 9.1

Factor $5$ out of $y^{4} \cdot 5$ .

$\frac{5 \cdot y^{4}}{x^{3} \cdot - 15}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $5$ out of $x^{3} \cdot - 15$ .

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

$\frac{y^{4}}{x^{3} \cdot - 3}$

Step 10

Simplify the expression.

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Step 10.1

Move $- 3$ to the left of $x^{3}$ .

$\frac{y^{4}}{- 3 \cdot x^{3}}$

Step 10.2

Move the negative in front of the fraction.

$- \frac{y^{4}}{3 x^{3}}$