Algebra Examples

$\frac{- 20 x y^{8}}{3 x^{- 4} y^{2}} \cdot \frac{- 5 x^{- 3} y^{5}}{{(- 2 y)}^{3}}$

Step 1

Combine.

$\frac{- 20 x y^{8} (- 5 x^{- 3} y^{5})}{3 x^{- 4} y^{2} {(- 2 y)}^{3}}$

Step 2

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

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Step 2.1

Move $x^{- 3}$ .

$\frac{- 20 (x^{- 3} x) y^{8} (- 5 y^{5})}{3 x^{- 4} y^{2} {(- 2 y)}^{3}}$

Step 2.2

Multiply $x^{- 3}$ by $x$ .

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Step 2.2.1

Raise $x$ to the power of $1$ .

$\frac{- 20 (x^{- 3} x^{1}) y^{8} (- 5 y^{5})}{3 x^{- 4} y^{2} {(- 2 y)}^{3}}$

Step 2.2.2

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

$\frac{- 20 x^{- 3 + 1} y^{8} (- 5 y^{5})}{3 x^{- 4} y^{2} {(- 2 y)}^{3}}$

Step 2.3

Add $- 3$ and $1$ .

$\frac{- 20 x^{- 2} y^{8} (- 5 y^{5})}{3 x^{- 4} y^{2} {(- 2 y)}^{3}}$

Step 3

Multiply $y^{8}$ by $y^{5}$ by adding the exponents.

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Step 3.1

Move $y^{5}$ .

$\frac{- 20 x^{- 2} (y^{5} y^{8}) \cdot - 5}{3 x^{- 4} y^{2} {(- 2 y)}^{3}}$

Step 3.2

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

$\frac{- 20 x^{- 2} y^{5 + 8} \cdot - 5}{3 x^{- 4} y^{2} {(- 2 y)}^{3}}$

Step 3.3

Add $5$ and $8$ .

$\frac{- 20 x^{- 2} y^{13} \cdot - 5}{3 x^{- 4} y^{2} {(- 2 y)}^{3}}$

Step 4

Move $x^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 20 x^{- 2} y^{13} \cdot - 5 x^{4}}{3 y^{2} {(- 2 y)}^{3}}$

Step 5

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

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Step 5.1

Move $x^{4}$ .

$\frac{- 20 (x^{4} x^{- 2}) y^{13} \cdot - 5}{3 y^{2} {(- 2 y)}^{3}}$

Step 5.2

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

$\frac{- 20 x^{4 - 2} y^{13} \cdot - 5}{3 y^{2} {(- 2 y)}^{3}}$

Step 5.3

Subtract $2$ from $4$ .

$\frac{- 20 x^{2} y^{13} \cdot - 5}{3 y^{2} {(- 2 y)}^{3}}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Cancel the common factor of $y^{13}$ and $y^{2}$ .

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Step 6.1.1

Factor $y^{2}$ out of $- 20 x^{2} y^{13} \cdot - 5$ .

$\frac{y^{2} (- 20 x^{2} y^{11} \cdot - 5)}{3 y^{2} {(- 2 y)}^{3}}$

Step 6.1.2

Cancel the common factors.

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Step 6.1.2.1

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

$\frac{y^{2} (- 20 x^{2} y^{11} \cdot - 5)}{y^{2} (3 {(- 2 y)}^{3})}$

Step 6.1.2.2

Cancel the common factor.

$\frac{y^{2} (- 20 x^{2} y^{11} \cdot - 5)}{y^{2} (3 {(- 2 y)}^{3})}$

Step 6.1.2.3

Rewrite the expression.

$\frac{- 20 x^{2} y^{11} \cdot - 5}{3 {(- 2 y)}^{3}}$

Step 6.2

Multiply $- 5$ by $- 20$ .

$\frac{100 x^{2} y^{11}}{3 {(- 2 y)}^{3}}$

Step 7

Simplify the denominator.

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Step 7.1

Apply the product rule to $- 2 y$ .

$\frac{100 x^{2} y^{11}}{3 {(- 2)}^{3} y^{3}}$

Step 7.2

Raise $- 2$ to the power of $3$ .

$\frac{100 x^{2} y^{11}}{3 \cdot - 8 y^{3}}$

Step 7.3

Multiply $3$ by $- 8$ .

$\frac{100 x^{2} y^{11}}{- 24 y^{3}}$

Step 8

Reduce the expression by cancelling the common factors.

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Step 8.1

Cancel the common factor of $100$ and $- 24$ .

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Step 8.1.1

Factor $4$ out of $100 x^{2} y^{11}$ .

$\frac{4 (25 x^{2} y^{11})}{- 24 y^{3}}$

Step 8.1.2

Cancel the common factors.

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Step 8.1.2.1

Factor $4$ out of $- 24 y^{3}$ .

$\frac{4 (25 x^{2} y^{11})}{4 (- 6 y^{3})}$

Step 8.1.2.2

Cancel the common factor.

$\frac{4 (25 x^{2} y^{11})}{4 (- 6 y^{3})}$

Step 8.1.2.3

Rewrite the expression.

$\frac{25 x^{2} y^{11}}{- 6 y^{3}}$

Step 8.2

Cancel the common factor of $y^{11}$ and $y^{3}$ .

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Step 8.2.1

Factor $y^{3}$ out of $25 x^{2} y^{11}$ .

$\frac{y^{3} (25 x^{2} y^{8})}{- 6 y^{3}}$

Step 8.2.2

Cancel the common factors.

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Step 8.2.2.1

Factor $y^{3}$ out of $- 6 y^{3}$ .

$\frac{y^{3} (25 x^{2} y^{8})}{y^{3} \cdot - 6}$

Step 8.2.2.2

Cancel the common factor.

$\frac{y^{3} (25 x^{2} y^{8})}{y^{3} \cdot - 6}$

Step 8.2.2.3

Rewrite the expression.

$\frac{25 x^{2} y^{8}}{- 6}$

Step 8.3

Move the negative in front of the fraction.

$- \frac{25 x^{2} y^{8}}{6}$